If I unlock an encrypted wallet for 359711509437336256 or less seconds, I can sign transactions with it:

$ bitcoin-cli walletpassphrase "$x" 359711509437336256
$ echo $?
0
$ bitcoin-cli signrawtransaction $tx | grep complete
  "complete": true

But if I unlock it for 359711509437336257 or more seconds, it appears to have unlocked but I can't sign any transactions:

$ bitcoin-cli walletpassphrase "$x" 359711509437336257
$ echo $?
0
$ bitcoin-cli signrawtransaction $tx | grep complete
error code: -13
error message:
Error: Please enter the wallet passphrase with walletpassphrase first.

I don't know the significance of that number. It's nowhere near a power of 2.

I was trying to unlock the wallet effectively "forever", so put a big number. If I use too big a number (2^63 or more) I get an error message JSON integer out of range but for numbers between 359711509437336257 and 2^63-1 inclusive I get no error, but no actual unlocking.