Why does my oil light in my 2004 jeep liberty remain on when I first start my car?

The light will then turn off after re-starting the car. The car has been doing this for a little over a month off and on. I have been getting oil changes every 2,000 miles hoping to cure the problem. The Jeep is idling and running very rough and the transition between gears is very harsh.|||What weight oil are you using? In cold weather you should be down to 5W-30. If that's not it get the pressure read by a reliable gauge to make sure its not the sending unit, if that checks out, it could be an internal problem, sludge, weak oil pump, worn main bearings, etc.