I think it would be very difficult, though you could create a world where it could occur.
If we may work backwards, the tremendous ubiquity of sexual reproduction should be a strong indicator suggesting that there's an advantage to it over other reproductive approaches. Indeed, we see sexual reproduction later in the evolutionary tree than other approaches such as isogamy, which suggests that it has a higher fitness for reproducing "advanced" organisms than other approaches.
Now I won't be able to bring up a full scientific argument for why this is so. Sexual reproduction is buried so deeply into the genetics of our ecosystem that it would be folly to try to claim to have "the one reason" why sexual reproduction works better. However, with a little hand waving, we can try to build enough of an argument to build a world which stymies these advantages, leaving readers to ponder whether it is indeed possible.
If I wanted to grab the biggest part of the advantages of sexual reproduction in one topic, to make it easy for a reader, I'd say the big advantage is differentiation. Sexual reproduction creates a very strong opportunity for differentiation into two different classes of individuals with common DNA between them. If there is value in differentiation, this provides a powerful place to do it.
I think we can generally say that any sufficiently hostile environment to make an interesting story (say, Australia) is going to select for differentiation. It's just too useful. However, perhaps your planet can cause differentiation to happen later.
For expository purposes, let's call the two differentiated sides of your species masculine and feminine. We H. sapiens are familiar with the meaning of those gendered terms, so it's convenient. Now what if your planet had a long chaotic cycle, on the order of 30-50 years. Perhaps its weather, or maybe it's some alignment of some god-awful trinary star system (the stability of which is a separate question). Regardless, it may be very effective to have a large number of non-sexed children, waiting to see what the planet does before adjusting the mixture of masculine and feminine to fit. Maybe 10 years into their life, we find that the planet has created an ecosystem where boisterous strong stubbornness is needed. Then an entire generation can take the path towards the masculine side right then and there.
If your species took this path, it would have to take care not to rely on sexual reproduction. If the phases of the planet demand a vastly masculine approach, there may not be enough females to sustain the population. Likewise, if the population needs to be mostly feminine to get through a subtle crisis, there may not be enough genetic diversity left in the few masculine individuals. This would create a strong incentive for the species to be able to mate regardless of such a gendered arrangement.
The price, of course, would be that the differentiation happens later. If there were value in differentiating early (such as teaching one half of the species child rearing from day 1, literally), then that would encourage sexual differentiation. Since you don't want that, you need to make sure that there's value in waiting until you have more information about the perils that your species faces. That'll ensure there's selective forces to make the differentiation happen late.
If the planet isn't enough of a force to compel your species to evolve for late differentiation, you can always borrow some spiders from Australia. I don't know if a swell of spiders will encourage masculinity or femininity, but if you'll excuse me, I'm going to go jump in my wife's arms now while shrieking like a little girl.
(Credit: National Geographic)