pump will not stay primed

I have an above ground pool and my pump has a good suction but will not stay primed with the skimmer basket in. It will run for a few min. and then as the water spins it creates a hole for the air to enter, and it is only pulling water in through the center of the cone and not through the hole basket. The water level in the skimmer is at least 1/2 to 3/4 full. The basket is broke around half the top and also has the 1" 1/2 cone in the center I can cover the top of the cone with a leaf or hand and the pump looses prime even though the rest of the basket is clean. I can take the basket out and cover the hole in the bottom of the skimmer housing and it does not loose prime but will pull my fingers through the pipe if I leave there to long. I do not have any leaks in the pipe and the clear top on the pump filter seems to be sealed good.I guess my question is could the broken basket be causing the problem?