Depends how obsessive compulsive you are, I find.
If you happen to have a lot of spare time and just want to always have a nice cleaned out mechbox, I'd say go ahead and do it after every game if you want to. Within my team i offer to clean out entirely the mechbox, make sure shimming is right, and then relube everything with white lithium grease. Although this isn't needed, some people just prefer it. After every game I clean my mechbox entirely. White lithium grease isn't expensive, you can buy it in a 200g squeeze bottle for like $5-$10 I believe? That much also can last an individual person who cleans their rifle every week a fair amount, let's say 6 months to a year as long as you're not plopping it in there.
Whether you're obsessive or not, as mentioned above, you should always clean out your barrel after (and before if you're that concerned) every game. If you don't actually have barrel cleaning rod, just get a metal coat hanger, fold over the tip enough so it can fit without causing a tight fit, and wrap some soft kleenex around it and give it a couple good pass-throughs. I personally do that, as well with dipping the other end in candle wax so when it passes through entirely you don't risk it scratching the barrel.
Primary: Custom WE M16A3
Secondary: KWA MP9
Side: Custom WE M1911A1