Oil pressure PSI gradually goes back to zero.

I am driving a 1992 Subaru Loyal wagon with a 1.8L engine. The original engine was burnt in Jan 2005 with 110k miles. A used engine exactly for this car was installed in June 2005. The vendor said the used engine had only 40k to 50k miles. The mechanics who installed the used engine did not move the "oil pressure gauge" from the burnt engine to this 2nd engine that came with "oil pressure switch". After I got the car home, I took the "oil pressure gauge" from my burnt engine and installed on the 2nd engine. Now the problem with the 2nd engine is: after I started the car, the oil pressure meter showed the PSI built up to 18 PSI (the highest) in a few minutes. Then the PSI started to drop. After I drove it for 10 minutes, the PSI went gradually back to zero and stayed there. Then I could continue to drive the car for one or two hours and seemed no problem. The only use of the car is to make a trip of 115 miles (one way) once a month. It made the long trip with zero PSI. It has been like this for over a year and the only noticeable problem is my car burnt one quart of oil every 150 miles. I only drove about 1500 miles over the past year. I am wondering how serious is my oil pressure reading problem? What components could be faulty? What potential damage it could cause? Thanks.