Mods are essentially unlimited in terms of deletion and undeletion. Mods have a great deal of power, and often need to make judgement calls. Mods are human exception handlers and posts like this could be considered an exception
I've personally suspended a user for mass vandalism of of his own answers. Suspensions are also meant to let users cool down, though with varying degrees of success. Cooling down is good, even without one.
Personally I consider my answers part of the commons. I have the ability to improve on them, prune away ones that are patently incorrect (and I would do this - and it would be something to let a mod know), and as I always tell others You are not just answering for the OP, You are answering for the next person with the problem.
Can someone please tell me if that decision is legitimate
I have no idea. Depends on your reasons too, and there's no boilerplate, standard answer here.
if/how one can challenge it
Talk to the mod. Bring it up on the per site meta and make a case for it there. This also means there's a clear trail for others to follow. However don't make this a rant, give clear coherent reasons outside "its my answer". In fact a good strategy for this would be write it from the perspective of another user.
what happens if one deletes the answer again?
Deleting and undeleting the answer repeatedly is just messy. At some point you might choose to
Let the wookie win just step aside, and decide its not worth the annoyance. Of course, at some point after step 2, this might happen naturally with proper perspective.
That said, in the final estimation, it really depends on why the post was deleted or undeleted. If its a reaction to a deletion out of anger or annoyance, I can totally see a mod justifiably doing this.