Is it possible to extend an AFSP training request?
Assuming that you're in category 3 (aircraft under 12,500 lbs) then an approval is only valid for 365 days, so if you want to continue flight training after that then you need to request a new one:


  Once you have permission to train, you have 180 days to begin training
  and 365 days to complete the approved training. Both of these time
  periods start from the day you receive approval. For example, if you
  begin flight training 30 days after you have been approved, you now
  have 335 days to finish. If you do not finish, a new training request
  must be submitted.


That's from the AOPA AFSP guide; the TSA's own AFSP webpage is a bit more difficult to use.