I think Leebo's comment may be misleading. The cover doesn't put any extra strain on the pump and the water is still circulating under the cover just fine.
The skimmer takes in debris floating on the surface of the water, so with the cover on the skimmer has a "hard time working well" in the sense that all the debris that would have fallen in the pool is now sitting on the cover.
Remember that, depending on how you remove the cover, much of that debris will end up falling in the pool. I use a cover roller, so when I remove the cover all that stuff falls in the pool. There is also some debris that gets in around the edges. If the cover has been on for more than a day or two I will run the cleaner once the cover is off, which also has the effect of allowing the skimmer to clean up the surface.