The answers ranged all the way from "every time I shoot it, even if it was only a few shots" to "never, unless it starts to malfunction". There were some owners who claimed that they had owned a Ruger 10/22 for many years and never cleaned it.
While I wasn't one of the guys referred to above, I am one of the guys who is in the "about never" camp. However, there is cleaning, and then there is
cleaning.
Can you damage a gun by overcleaning? Abso-frackin-lutely!
If you do something wrong, use the "wrong" equipment, do it carelessly, etc. Run a steel rod down the muzzle like you are pumping the handle of a water pump, odds are good you are going to damage the crown at some point. Constantly taking apart and putting back together guns not designed for that, things get worn prematurely. Modern military firearms (1890s on up, and excluding revolvers) are designed with the understanding that the military troops will take them apart and put them back together all the time, and under less than perfect conditions, often without the proper tools, and sometimes without the proper skills.
Commercial sporting firearms are often not made with that in mind, and over-frequent disassembly can cause problems.
We live in an era where our ammo is (generally) no longer corrosive, so cleaning after shooting is not the necessity it once was. (it still is, if you shoot corrosive ammo, though)
.22RF barrels often behave differently than centerfire barrels. Almost exactly the opposite. With a centerfire barrel, we clean the bore to restore accuracy. Often we clean it before accuracy falls off, so that it doesn't.
A .22RF barrel can often LOSE accuracy when cleaned. Clean a good shooting but dirty .22RF barrel and often groups get bigger!!! And they usually stay that way until enough shots have been fired to dirty up the barrel again. Some call it "seasoning", it is an often observed fact that it may take a couple hundred rounds though a cleaned .22RF barrel before the accuracy returns to what it was before the cleaning.
SO, there is that to think about, for the bore. Next is the rest of the gun...
As an experiment, I let my 10/22 go for 10 years without cleaning it in detail. I didn't keep a round count, the rifle wasn't fired a lot, but did get several thousand rounds a year. I did not clean the barrel at all, and I did not take the gun apart in any way. I did wipe clean what could be reached with the action locked open.
The rifle never malfunctioned in any way during that entire time. Accuracy never changed. Then, after 10 years, I did do a full takedown and clean (other than the bore). The entire inside of the action was coated with powder residue, 1/4" to 3/8" thick!! Except where the bolt moved, there it was thinner..
Incredibly filthy, but the gun still ran flawlessly.
Your rifle may behave differently, I'm not saying all of them will be the same as mine, but I think most will be about like mine, if treated the way I treated mine. So, I'm in the "don't clean it until you need it" camp for the 10/22.
other guns will need a different level of care. Wipe out the action, keeping the barrel breech and boltface clean, the gun will run fine for an amazing amount of time without any other cleaning. Clean the bore if you think it needs it, I rarely do, but that's just me, and I'm lazy. your barrel might shoot as well after cleaning as it did before, mine usually don't....My .22s are plinkers, and small game guns, not match rifles, and I don't shoot match quality ammo, so I don't worry about getting the nth degree of accuracy possible.
Now, if the gun gets soaking wet, dropped in a puddle, etc, then a detail strip and clean is called for. Otherwise, I don't think your 10/22 needs detailed cleaning until/unless it starts failing.
Just my experience, and opinion, and worth every penny you paid for it!