1991 Ford Explorer burned starter relay and starter motor

My daughter has a 1991 Ford Explorer which has only 110000 kms. One day out of the blue she experienced a slight problem starting the vehicle. The car labored briefly and then turned over and started with no problem. About two weeks after the incident, after driving home from work her alarm monitor was making wierd noises and when she went to the car it was very apparent that something was burning. We disconnected the battery and later discovered that the starter relay was frozen shut and the starter motor was also "fried". I went out and purchased a new relay and re-manufactured starter and the car was fine for two days. Then the problem recurred, relay and starter fried. What could possibly cause this? Was one of the two products purchased faulty? The shop where they were bought is closed for the holidays and she needs the car but I am afraid to go through the same procedure and have the same thing happen. Any ideas on this, could a low charged battery be the cause. When the new starter and relay were put in the car fired right up without a problem.