Do you know what your CYA reading was when you closed the pool last fall? A lot of pools have CYA degradation over the winter which results in ammonia which takes a lot of chlorine to break down.

As far as it being the fault of the cover, all covers have their inconveniences. Another option is to not cover it at all in the winter. I don't and neither does Poconos (another of the mods). He has really cold snowy winters up in NE Pennsylvania maybe similar to what you have. I just keep after the pool in the fall, scooping out all the fallen leaves and then shock the pool and raise my pH up to around 7.9 before I lower the water level below the returns and then disconnect the equipment. In the spring, I do have some dirt on the bottom of the pool but that is easily vacuumed out. The water stays clear. I do hook my equipment back up pretty early because the weather gets hot here pretty quick and I need to start being able to chlorinate. Just throwing another option out there for you.