Yeah, it's a good idea to check this with your DM first. As written, there is no rule for replacing psicrystals (there is such a rule for familiars). It could simply be missing, or they just assumed, that everyone knew that it was the same as with familiars, or whatever, maybe it's even meant to be only one psicrystal ever.
But... there definitely is no rule that allows you to replace the psicrystal when you lose it.
Therefore it's a good idea to ask the DM how this will be handled, before getting one.
Bye
Thanee
P.S. And yes, you need the feat to get one.