My pool pump will run fine once I prime the system from the top of the pump basket. Then once the timer shuts the pump off, when it trips the switch to run again there is no water in the pump and it cannot gain its prime. Do I have an air leak or are there check valves that are not functioning properly that is allowing the water to run out of the pump and lines when it is shut down?

If you are a long way above the surface of the pool and you have a leak on the filter it could be a check valve problem.
With it competly loosing the prime it sounds more like a suction leak. This will be in the plumbing and will need a re-plumb or it could be as simple as a lid "O" ring or cracked lid.
What happens is the air get's in the tank and air will compress when under pressure. Then when the pump shut's down the air can expand again. When it does it will rush back through the system and blow the prime right out of the pump. Quite often you will see water blow out of the skimmer or just blow the skimmer lid off. I hope this helps. Good luck.