Yes
Bear in mind that what you're looking for must, of necessity, be entirely contrived. That's because developing planetary economies for even one world is a bit beyond the scope of Stack Exchange (the book rule). However, I believe that in a general sense, a contrived solution can be had.
Conditions
A post-scarcity economy is almost never what people think it is. It is not a condition where everything anybody could ever want is provided for them free of charge. In fact, a post-scarcity economy is no more likely to bring about a utopia than any other economy. This is because it is impossible for everything to no longer be scarce. Every planet has limits. Limited mineral and agricultural resources (or, at least, limited access to those resources) are the most common problem.1 What could be true is unlimited energy and information/education. Possibly basic foods and enough resources for very basic needs (a clothing allotment, basic housing,2 etc.). The problem arises when somebody wants prime rib, but it's impossible for everyone to eat prime rib whenever they want. So, we must admit that there's no such thing as universal post-scarcity. This is a good thing. It's what will make your story work.
A depression occurs when, for whatever reason (too much unemployment, locked up credit - e.g. lending institutions become land rich and cash poor, or an upside-down supply-and-demand curve for critical resources, etc.) money stops moving or its value drops in an economy. Most people don't realize that it is not the presence of money (or even value) that drives an economy, but the movement of money (spending it...) leading to the production and/or improvement of things (real property, research, trinkets to buy, etc.), which leads in its turn to establishing the value of money.
In your case, a depression caused by the advent of a "post-scarcity economy" must of necessity mean that there was a massive jump in the efficiency of automation leading to many of the basics people need to live being suddenly inexpensive to acquire. One would think that the drop in price would strengthen the economy (and normally it would), but in this case, it also requires an absolutely massive loss of jobs — mostly manufacturing and its administration (the chain reaction would be staggering). That's the only way I can see to get a depression out of a post-scarcity economy (even at the beginning). This means that a huge percentage of your population is suddenly on the dole, and it's not their money (through employment) that's paying for the post-scarcity goods, but inflationary spending by the government. Nasty.
The crisis
I believe it is believable that Earth's planetary government would react to this problem by leaning on its colonies to stem the tide of economic depression. What are they asking the colonies to do?
Employ people. Earth suddenly has too many people and it's a bit awkward to celebrate the advent of a post-scarcity economy with a war (the government wants one, it's desperate for it, but it can't start it... more about that later). So, Earth is willing to reduce tariffs on imports and decrease the costs of her exports, so long as the colonies implement massive emigration-based employment initiatives.
Buy stuff. Earth can't reduce the cost of those exports too much, because what they need is for the colonies to take over the "move the money around" job that is usually the duty of employed people. That means production doesn't drop in value even while it's ramping up substantially due to the tech that brought about the post-scarcity economy.
And, just because it tickles my recent-history conspiracy funny bone...
- Finally, Earth knows perfectly well that they can't foist enough people onto the colonies to fix the problem. Worse, the more they ship out, the more dissatisfaction with Earth increases because people emigrating from Earth will naturally feel they have the right to enjoy the post-scarcity economy — and getting shipped off to the colonies means one can't enjoy it at all (i.e., the people don't want to go. Who would when the government is paying you unemployment?). But the unemployed have gotta go. Thus, a manufactured plague is created to thin the population that won't ship out.
Secession...
Now, let's look at all that from, say, Mars' point of view.
Earth suddenly has a technology that seriously sets her ahead in the political-strength race. If she can provide for at least the basic needs of her people, she needn't depend on the colonies to help with that. So, the colonies see a future where Earth's imports are likely to drop, which will affect their economies.
Earth's efforts to stem the tide of the economic depression puts a considerable amount of stress on the colonies. Accepting all those emigrants and the demands for Earth-based investment and the colonies' own imports quite literally threatens to drag the colonies into Earth's economic depression.
Finally, that plague is no small thing... and Earth just demanded that plague-ridden zombies a potentially exposed population be welcomed into the colonies.
Conclusion...
Slam the gates shut. No new emigration, conversion to an introverted economy that depends less on Earth, meaning shifting jobs from export-related employment to self-sustaining employment. And keep the money in the colony. (Mars first!) Increased military spending can help make up for the loss of Earth-bound exports and the swift negotiation for a league-of-planets-except-for-Earth coalition immediately starts.
But there's something you can't ignore...
Secession is not something any government is willing to put up with. The moment the colonies secede, it'll start a war. It always starts a war.3 And to make things worse... Earth wants a war to thin that unemployed population and to generate new jobs to replace those lost to the shift to a post-scarcity economy. Earth will be looking for a reason to fight, she simply doesn't want to be perceived as wanting that fight. The colonies just handed her the solution to her economic problems on a silver platter.
And that's why the idea of post-scarcity economies leading to utopias is, in my personal opinion, breathtakingly short-sighted. What such an economy really creates is a deeper class separation between those who are forced to depend on the post-scarcity basics and those with enough wealth that they can enjoy the obviously scarce resources that are unavailable to the rest of the population. It's a nice idea... but it's an unstable economic condition that's far more likely to result in revolution than it is universal peace.
ONE MORE THING... Now that I've finished writing this, I just realized (with no small amount of embarrassment) that what I've done is develop a significant portion of your plot for you. That is NOT worldbuilding. That's off-topic (too story-based) storybuilding. In other words, this question should have been closed.
Why is it storybuilding and not worldbuilding? Because you're asking us to help you rationalize a choice made by your colonies. Per the Help Center, questions about the choices of individuals and organizations are off-topic.
Also per the Help Center, we're here to help you build your world, not to tell your story. Please do not ask storybuilding questions. This was a freebie.
1 The problem most people who believe in the utopic value of a post-scarcity economy is that (e.g.) Star Trek-style replicators can't make anything out of thin air. An iron beam still requires iron. The manufacturing process may be tremendously simplified (and, therefore, access to the beam much simpler and its cost much lower), but every ounce of iron is still required. And with every beam in our example used for construction, more iron must be mined from the ground. That example demonstrates why post-scarcity economies cannot be utopic. There are always limits, always restrictions, and always scarcity. It's just that what causes the scarcity changes. However, this isn't the place for an in-depth analysis of the differences between an actual post-scarcity economy and what most writers think it is.
2 If you're not thinking the word "projects," then you, dear reader, really have a rosy view of what a post-scarcity economy can do. It can't provide everyone with five acres and a 3,000 square-foot house in the Hamptons. Post-scarcity housing must take the form of housing projects (large apartment buildings), better known as human warehousing. Re-read footnote #1.
3 Secession that doesn't lead to a war is called negotiated independence. But in the case of a government suffering from an economic depression, no such negotiation would ever be permitted unless the regions seeking independence were a substantial part of the economic problem.