Land Rover Repair: Engine issue, oil pressure switch, highway trips

Question
We have a 99 Disco 1, 160k, run great except on highway trips.  after driving for and hour or two, oil light starts flashing, engine loses power & runs rough.  Pull off and turn off the engine.  Restart and it's fine but may or may not happen again with in 15 mins.  Let it sit for 20~30 mins, it will go for an hour or two. We have never experienced this around town. Could it be connected with the alarm? just asked this because we can't get the alarm to go into the programming mode for a remote (both remote were lost).

we have replaced the oil pressure switch already, no joy. Unplugged the hood switch, my son made it back to collage without having to stop (2.5 hrs, did it thinking the alarm is trying to immobilize the truck).

any suggestions?

Answer
It sounds like the oil pump is failing, and it's important to attend to that because its failure will ruin the engine.  With what you have told me, my next step would be to pull the front cover off the engine and look carefully at the pump.  Then I would pull the bearing caps and check for damage.