Our air conditioning was working fine until last week. Now after it is on several hours the blower quits running. The air conditioner is still running. I shut the whole system off for an hour or so and the blower on the furnace comes back on. We had the relay switch replaced last winter when the blower would not run.

Nothing provides more job security for electricians than the common relay. It could be bad again. On the other hand, it sounds more likely it is a overload built into the blower motor. If the motor is getting old and drawing more current because of a dry bearing or partly shorted windings, it could get hot and the circuit breaker like overloads in it open. Once cooled, they close themselves. Next time the blower stops, check to see if you have power to the load side of the relay. A few drops of oil in the bearing might be all it takes. If you are more adventurous, sometimes you can even lubricate a bearing that was not designed to be lubricated. If the blower is belt driven, the offending bearing may be on its shaft. Identify dry bearings by turning the blower its self by hand. Little or no resistance is more likely to be a problem than a light, but smooth resistance. A dry ball bearing turns easier than a lubricated one cold, but heats up builds resistance.