I'd say it'll probably remain canon just not discussed often, since even if it was still available it is still a children's show. There might be Easter eggs and references to it though, like how the Ghost from Star Wars Rebels (a kids Star Wars show) shows up in Rogue One a few times but isn't focused on or talked about
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It's canon until it's not (ie, explicitly contradicted by some other Trek installment). And even then, canon in fiction is rather a silly concept anyway, and is largely more up to the collective opinion of the fan base than whatever big corporations owns the rights to it.
Canon Trek is rife with contradictions. The rest of your comment is a healthy approach to thinking about canon, though.
Prodigy is canon insofar as everything is canon when it happens on screen. I like to think of the canon containing all Star Trek works right down to your fan fiction novel or your "head canon" with some things being more canonical than others and with those things which are seen on screen either as a film or TV episode are the most canonical of the canon. Prodigy still fits that bill. I doubt that there will be anything as canonical that would "undo" what Prodigy did. But if that happened we would just incorporate the conflict into the canon like we always do.
I like to think of the canon containing all Star Trek works right down to your fan fiction novel or your "head canon" with some things being more canonical than others and with those things which are seen on screen either as a film or TV episode are the most canonical of the canon.
This is how Star Wars Expanded Universe canon worked before the Disney acquisition and canon wipe. Every piece of Star Wars media (movies, TV, books, comics, games, etc) was some form of canon, but there existed different tiers of canon, with the movies in the top tier. Everything in any tier was considered fully canon, unless it was directly contradicted by something in a higher tier. I thought it was quite a cool system.
After the Disney acquisition, they switched to a binary form of canon - the movies, the 2008 Clone Wars show and everything subsequently produced by or under license from Disney was canon; everything else (including decades of Expanded Universe novels) was not.