These days they are selling Intex pools with very small filter pumps I have noticed. I have a size B larger filter with my pump and wash it out good it out atleast twice a day, more often if there are special circumstances. I don't think you can overdo it with washing out the paper filters. And I replace the filter every week to 10 days with a new one. The only thing I have ever had trouble with the filter not catching is sand that is too heavy to be picked up by the water flow.
Also if you aren't doing it already, make sure when you get ready to restart the filter pump after washing the filter, to unscrew the thing on the top and leave it unscrewed until only water comes out of the top of the pump. I went a good two years not knowing to do this lol. It raises the water level up higher onto the filter.
Another thing is to make absolutely certain that you have no air leaks around any of the fittings, check the hose clamps and O Rings and such really good, even a tiny air leak in there can reduce the power of your pump and filter. Often water will not be leaking especially on the hose connection bringing water from the pool to the filter, but when it gets to sucking good, it will pick up a little air. If there is a water leak, even a small one, it can really reduce your power.
And sometimes you just have a pump that does not work as well as it should, even if it is brand new.