Just from a practical standpoint, I'd think they'd be valid until the estate was settled.....
Rarely, we see "temporary" Letters Testamentary, that have an expiration date. I can only guess that there was an urgent need to settle some portion of the estate while the final Letters were being processed through the court. But those are very clearly marked as "temporary" and have a specific expiration.
As this is Probate, it will probably vary by state. I'm in Calif.
Just a lowly 1st Year Law Student ("1L"), so don't take anything I say seriously!