Hello; These above posts tell the tale. There are two sorts if filter media. If you remove too much of one sort then the tank will go into a "mini-cycle" that will have ammonia levels up for a few days.
Hello; I also feel that larger and more often water changes (WC) are needed. How much and how often is hard to determine. One way is to use the water quality tests as a guide. When the ammonia and nitrites are at zero then find a WC schedule that keeps the nitrates at or below 20ppm. Some use 40 ppm as an upper limit others try for much lower levels. From my reading of threads it seems that lower is better but also that 20 ppm is a more common goal and it is reported that tanks run OK at that level.
Back to filter media and the need to clean a dirty filter. You are likely best served by having two sorts of filter media. The first type is the floss or some such designed to trap crud out of the water. I think of this as throw away media. I usually place this sort in a filter so it gets the water from the tank first. I do toss this sort of filter media.
Much will depend on the sort of filter you have. If of a large capacity then you should have room in the filter body to have a second sort of filter media. I and others call this the bio-media. It is designed not to trap crud but is designed to have a lot of solid surface area. It is usually placed behind the floss type so that the floss protects it from the crud.
The job of bio-media is to be a home for the beneficial bacteria (bb) that do the tank cycle stuff for us. The bb are sessile ( learned this term on this forum). This means they make colonies that stick to solid surfaces by way of a slimy or sticky layer. These bb need to have water flowing over their surfaces.
While there can be a lot of the bb on bio-media in a dedicated place in a filter, the bb also will exist on most any surface in a tank. In the tubing of the filter system, on substrate, on décor and so on. My guess is the limiting thing being the amount of water flow.
I toss away the first type of filter material when clogged up. I try to do this in stages. In some filters there are two chambers. So I toss the floss from one chamber on one day and from the other chamber days of usually weeks later.
For the bio-media I do as suggested. If it gets clogged up with junk I rinse the junk away in tank water during a WC. The sticky bb film will stay attached to the media.
