Debbie,
What pumpkin puree are you using, canned or fresh? Are you making the crust yourself or store bought? Tell me about your ingredients and perhaps I, or someone here, can come up with a solution.
Too much moisture in the pie can cause this. Try wringing out all the liquid from the pumkin puree that you make and use just the right amount of milk (not more) that the recipe asks for. Don't refrigerate when the pie is hot or warm. Let it cool completely on your counter.
This is probably unconventional, but I made a pumpkin pie last week and put the pie base on the top of the pie, instead of the bottom. Not only did the pie not separate from the base but the base was nice and crispy and golden, instead of soggy as it would be if I put it under the pie filling.