...If your pump is running and when done there is little water left, then you have a small tear in the cover. This means you finished and came back the next day to water back on the cover. You can leave the cover on, just allow the water to fill up. In the spring, pump water off the cover and back into the pool. As you are pumping water off, have a helper pull the cover on each side and support it so the cover is above the water line or you will be siphoning water from the pool (happened to me). Then you can either repair the cover or replace it.
... If your pump is running and the water is still on the cover, then you have a large tear in the cover. The cover should be replaced at this point. You could leave this on during the winter, just do not remove water unless it is extremely high in the pool. The water will also act as an insulator for the lower part.
This year, what I have done is created a lot of slack in the deep end and by the steps so water can stay in this area. Covers have a tendency to rip in areas where they are being pulled (like a 90* degree corner), which you could place some foam padding, etc. I gave enough slack so hopefully there will be no problems.