What happens when the timestampers certificate expires?
You can extend this question to a more general one:
"Is a signature still valid if the signer's certificate expired?"
Well, it depends on which requirements are implemented by a validator.
Mainly the signer confirms the payload's authenticity, e.g. timestamp, with the signature. Some validators implementing certain signature standards consider any signature invalid in case any of the certs needed for validation expired in the mean-time. The reason is that the original assertion(s) cannot be longer securely verified because the formerly used crypto systems (e.g. signature algorithms, key-length) might have been weakened over time (better cryptanalysis). So these standards mandate that signatures have to be re-created every now and then. This gets very interesting if you think about archiving data for decades or centuries.
As an example consideration:
Would you still trust a code signature done with RSA-1024 and MD5 let's say 20 years ago?