how many times can i palingenesis

You can palingenesis till you reach lvl 100 or you run out of grails...

Assuming from their respective level caps:
1* = 10
2* = 10
3* = 9
4* = 7
5* = 5
If you are referring to the amount of grails you'll get in game, JP reportedly has had 27 grails, including story grails and event grails from the start of the game.

All info are taken from the fgo wikia.