I can't share the map, but the details aren't much more complicated that described unfortunately.
I have also tried on different maps.
I have a layer in a web map, I've added a filter but clicking "save" seemingly does nothing.
It's ok on one layer, i.e. the filter works and saves if I reload the map. However, on other layers I can set the filter, press save, then click on another layer only for the filter to disappear.
There is a UI/UX issue I think, the saced filter looks no different to a open editing filter. Screenshot below
The majority of mine have now saved, perhaps there was an AGOL flutter earlier. My layers were taking forever to load.
That being said, perhas the issue is more a UI one? It is hard to tell if a filter has in fact, saved.