The gas operating system between the Mini14 and the AR/M16 makes all the difference. It is not so much that the Mini14 isn't reliable, but rather it's not as accurate as the AR.
The Mini14 is a derivative of the M1 Garand action. There are more moving parts on the Mini14 which affects accuracy than on the AR/M16. First, the slide (as Ruger calls the operating rod handle) lockup must be consistent. We're talking about dirt affecting the lockup of the bolt, the possibility of the slide getting bent (which affects lockup, timing, reliability), pressure on the bolt from the bullets in the magazine (which also affects consistent lockup), uneven wear on the bolt lugs (resulting in canting of the bolt while in its locked position - this was also an issue with the M1 Garand, M14 and the M1 Carbine). There are other things affecting accuracy on the Mini14. One major thing is the barrel which is sporter weight and thin. Like other sporter barrels, once it heats up with sustained firing, it becomes like a spaghetti and the group will open. The other problem with the barrel is the mil-spec chambering which allows for looser tolerences than SAAMI. Ruger does this to accommodate all that surplus ammo we tend to shoot and to ensure reliability with that ammo. Of course, this doesn't make for match quality.
Turning to the issue of reliability, some of that is attributable to the shooter. I attended one class where a shooter's trigger assembly fell out. It was either due to improper reassembly or at some point, the trigger guard had been tweaked and until corrected, will not lock into the stock properly. A lot of reliability problems with the Mini may be attributed to after-market magazines. Face it, as a people, we not only enjoy precision shooting but we also love blasting for the sheer pleasure of it. Unable to get high capacity factory magazines (Ruger never made their own and they subcontracted out for its production) because of Ruger policy and the hi-cap mag ban (aren't we a safer and crime free society now?), many have resorted to after markets: some of which is fit only as scrap metal. Ammunition is another issue but Ruger generally tests its guns with all types of ammunition available on the market - including the surplus stuff all of us buy cheap. Ruger does this to test how their gun does with the assorted ammo on the market and to detect any problems (that way they can reengineer the gun - which hasn't happened all that much since its first inception). This allows Ruger to train its customer service staff when the calls come in.
Turning to the AR, it relies on the gas impingement system (which I believe was originally derived by the French). There's no op rod (slide) which affects lockup. Just the bolt carrier, bolt and the buffer with its spring. Fewer moving parts to go wrong. Further, barrels on the AR aren't difficult to change (just make sure the headspacing is good) and there's lots of heavy barrels which you can have match chambered. Oh, the barrel is easier to free float than on the Mini.
Addressing lockup, pressure from bullets in the magazine act on the bolt carrier and not directly on the bolt (more consistent bolt lockup). The multi-lug AR bolt doesn't have that offset camming problem mentioned with the Mini14/M1/M14 rotating bolt design.
The weakness of the AR design is its magazine. Those aluminum lips are easily bent and reliability may be compromised unless its corrected. Steel bodied Mini14 magazines are simply tougher.
While I find the Mini14 has greater eye appeal and is handier, especially to tuck behind your truck seat, its design doesn't compete against the AR for accuracy. Returning to reliability, I've never dunked either gun in mud to test it. Cared for and used with good ammunition and good magazines, either gun should give you years of shooting pleasure.
Sorry for windbagging.