A gear pump has some intrinsic internal leakage.
If you build up pressure in the discharge, then stop rotating the shaft, the pressure will decay, as the pumped fluid leaks back through the tooth tip clearances and the gear face clearances. This typically happens in seconds, for small pumps and small rigid downstream chambers.
A WORN OUT gear pump will have considerably larger internal leakage, and will eventually be unable to supply any given demand downstream, so the pump would "lose its pressure", hopefully over a period of years when pumping oil.
There is not nearly enough data visible here to say for sure, but it may be time to rebuild or replace your pump. ... OR your relief valve or whatever is 'set' to control the pressure, may be drifting, or worn out. ... OR there is a leak that you don't know about yet.
Mike Halloran
Pembroke Pines, FL, USA