or Stowe in Buckinghamshire/Northamptonshire, in Shropshire, in Staffordshire etc etc !

an example :-
For Stowe Bucks, I would expect Buckingham rather than Aylesbury as the Reg District.
however this might just be your man

Name: Andrew Graham
Year of Registration: 1845
Quarter of Registration: Jul-Aug-Sep
District: Aylesbury
County: Buckinghamshire
Volume: 6
Page: 312

If Father was still a soldier at that time, you might reasonably expect the birth to be in a garrison town rather than a small village in the FoD.

Any further clues ?