I recall a great many Youtube videos of trigger happy Americans testing the endurance of various guns under consecutive fire. Naturally, they'd most likely be using some AK rip-off, or modified civilian model, so take the results with a grain of salt.
In one particular instance, both the AR and the AK that were being tested took ~850-950 rounds before deforming and becoming useless. In the case of the AR, the hand-guard material caught fire and the gas tube deformed and separated, making the gun unusable. In the case of the AK, a similar story. At the 800 round mark, the hand-guard caught fire, however, unlike the AR, it failed due to a deformation of the barrel, which lead to an improper seal for the gas piston. I recall the uploader attempted to bend the barrel back into place and got about a dozen more shots off. Interestingly, the AK never cooked off.
The point being, in a worse case scenario, with fully automatic fire and no breaks, a modern, civilian-accessible assault rifle can get off about 850 rounds before some kind of serious failure.
In short, firing a small arm at fully auto for a long time is a lot like rev-ing your car in the red zone for a long time. In both cases the mechanism will operate to some degree, but ultimately you are spelling a short life expectancy for a marginal increase in efficiency / power.
I ought to add that the uploader was dressed in thick material, with a welding helmet and welding gloves, and still managed to comment on the heat emanating from the gun.