Will Artoria Pendragon (Santa Alter) come back again?

I'm sorry, but she won't.

The re-run has already passed, and given that JP has never had a re-re-run I think its very unlikely she will ever come around again.

No. There's the hope that they'll implement a way to obtain welfare servants that have already had their rerun (the RP store, maybe, since we'll eventually start getting RPs for NP6+ welfares), but if it happens, it'll be at least two years from now in NA.