If you want to keep it out of the hands of the poor you just have to make sure it never becomes cheap to use. Whether this is due to some factor in the operation of the device itself or due to manipulation is up to you.
Artificial gestation is inherently expensive
In order to gestate a human you need a lot of interesting hormones, nutrients and so on, all carefully balanced and so on. You'll need a source of compatible immune system components to ensure the fetus is born with a functional immune system. Synthetic amniotic fluid is devilishly difficult to create, and might require complete replacement on a regular basis. The exchange membranes on your artificial placenta are complex pieces of nano-engineering, possible involving some interesting meta-materials, and they need to be constantly maintained. Nutrients have to be carefully mixed and infused into the system. And don't forget the cost of the control equipment, nor the cost of running it.
All told the cost of artificial gestation might naturally be in the millions already, and that's just running costs. It doesn't include maintenance fees, setup costs and a number of other, less obvious costs.
And no, it's not covered by your health insurance.
Source materials are extremely rare
The various consumables that are required for the gestation process are the end result of many, many supply chains. Nutrients are synthetically created proteins, amino acids, lipids, carbohydrates... and a ton of vitamins and minerals. Any one of the components for the nutrient solution could be hard to acquire for some reason, and it's likely that you're going to have multiple thin and expensive supply lines for them.
Source materials are ethically questionable
You need white blood cells, which must be sourced from a genetically compatible donor with a healthy immune system. And you need to harvest them often. You also need a number of hormones that are not available outside the body of a pregnant human female. Perhaps you have to use actual amniotic fluid from the same place.
But extracting that amniotic fluid significantly endangers the donor's own pregnancy, and harvesting the pregnancy hormones is likely to result in developmental issues for the donor's child... if it survives. There are only two real ways to get your hands on those materials: buy them from the donor, or harvest them from unwilling subjects. Of course all the information on the process talks about proprietary synthesis processes, because you don't want the world to know what sort of monster you really are.
Sabotage the supply chains
If none of the above works for you, you can mess with the supply chains. Somewhere in the network of operations required to get your amniotic fluid, white cells, nutrients and hormones there are bound to be a few choke points. Choke them to the point that only a trickle of the required materials are even being produced, and most of the production is ultimately required for your artificial wombs.
Of course there's nothing saying you can't make a little profit in the process. Find a process that competes with the devices for a particular resource, then promote the hell out of it. Make it something that makes people happy, or has some significant social value. Your goal is to have it absorb most of the raw materials, leaving fewer for your gestation devices. Anyone attempting to set up their own competing womb would have to compete with two or more existing systems for resources. A thorny situation indeed.
Protect the process
Assuming that it exists in your world, the patent system might be a significant impediment. Buy up every relevant patent you can get your hands on, through shell and puppet companies of course. Regulate them, charge additional licensing fees, sue anyone who attempts to use your IP.
In short, use all the tactics of corporate warfare, up to and including the covert ones: blackmail, intimidation, bribery, smearing... the normal, ruthless tools of big business.
Make it horrifically unsafe
Make some intentional monsters and use them as advertising to show the dangers of the technology. Advertise some false numbers for how often it fails. Generally run an anti-PC campaign for the whole thing. Make sure that the public knows that this is a terribly risky system that only a few people are able to afford.
Yes, you can lie if you want to.
Retain some troubleshooting services
They're not mercenaries, they're professionals who get stuff done. Stuff like sneaking into warehouses and research facilities to retrieve or destroy important components. After all, if the machines never work they're going too stop trying.
There are bound to be other ideas that we haven't seen in the answers. Hopefully some of these ideas are of use.