I clean mine after I shoot it, or after its been 'in the field' for a few days. When I say 'after I shoot it', that may mean 1 shot or 40, depending on how the day goes (ie 1 shot at a deer or 40 shooting at prarie dogs). Are you using new ammuntion? a lot of old 7x57 ammo is pretty 'soft' jacketed. And copper fouling can be removed without scrubbing, there are a number of copper solvents that work really well, Hoppes in particular if thats available in your area.
A LOT of us hunters have switched to stainless rifles to save on weight, cleaning, rust resistance etc and my stainless rifle seems to be less suseptible to fouling than my old blue one. of course maybe my old rifle was just 'old'