Battery Capacity Question

I searched the web but could not find a decent answer to this question/scenario. Seems like a simple question though.

If I have a 2500mA-Hr 1.2V NiCd battery charged to 1.2V connected to a 250mA load, how long will it take before the battery voltage drops 0.2V to to 1.0V?

We are missing some information.
The 2500mAHr rating states a discharge voltage. It may be the 1.0V you stated but it may be 0.9 or lower. This makes a difference.
The 2500mAHr rating states what current the battery was discharged at. Some times it is at the 10 hour level but that depends on the battery.
In you case it probably will take 10 hours.

The cell voltage under load depends on the internal impedance of the cell.