97 ecilpse Oil Pressure

I have a 97 spyder eclipse gs-t 2.0 automatic.

I have noticed the oil pressure is always normal when I first start the car and the engine is cold. Car runs good and shifts at appropriate times.
When 5 or 10 mins pass by of driving and my engine is at normal temperature, the Oil Pressure deacreses substantially. It does affect the cars shifting times and is noticeable.
Should I be worried? Or is this normal in older cars?

I was thinking of getting the oil pump taken looked at.

The car has 115,000 miles on it.

Any suggestions:

Thanks
Raul