Why is my 20A breaker not tripping when my clamp meter reads well over 20 amps?

The short answer is that your breaker likely hasn't tripped because of the specific curve it follows. Most standard breakers are thermal magnetic devices, and they are designed to react to prolonged heat buildup rather than an instantaneous spike. A high current reading, like 28 amps on a 20 amp rating, is definitely an overload, but the time it takes to trigger depends heavily on how much higher that current is than the rating. The manufacturer's trip curve graphs show that for a load only slightly over the rated amperage, the delay before the trip can be quite long.

Running an AC unit at that level of current for an hour is far beyond what that breaker should handle continuously. If it were a short spike, it might not matter, but this is sustained. Even though your meter is accurate, you are likely stressing the breaker and the wiring significantly. These devices are rated for continuous use at 80 percent of their capacity, meaning 16 amps for an extended period, not 28. Given that it has run for an hour without tripping, there are two main possibilities. Either the breaker itself is failing and is stuck in a non-tripped state, or the AC unit has an internal issue causing a huge and sustained draw. You really should pull the unit and inspect the compressor or the capacitors. Regardless of the cause, you need to replace that breaker with one rated for the actual load, which means sizing the breaker to the unit's full requirements, not just the old rating, or find out why the unit is pulling so much current.

Funny timing, I chased something like this last summer on my garage compressor circuit. Turned out my cheap clamp meter was picking up the inrush every time the motor kicked on and averaging it weirdly. What actually settled it for me was borrowing a proper true RMS clamp meter from a buddy, and the reading dropped way down once I measured over a few minutes instead of a quick glance. Mine was also an older unit with a failing start capacitor that made it draw heavy for a couple seconds at startup. Worth checking if your reading is steady or bouncing around. If it holds rock solid at 28 while running, that's a real draw and the earlier poster is right about the wiring getting stressed.

Been doing this since the days we actually pulled fuses out of a panel and carried them to the hardware store to match the size. One thing folks forget is those old thermal breakers trip based on heat, and heat takes time to build up in that bimetal strip. A load sitting a bit over rating can hang on for a good while before it lets go. That said, an hour at nearly 30 amps would've tripped every breaker I've ever swapped in. I'd kill that circuit tonight and check the run capacitor on the unit. A weak cap makes the compressor hog current, and it's a ten dollar part most of the time. I've replaced a pile of them with nothing but a screwdriver and a discharge stick I made from an old screwdriver and a wire.

Update: borrowed a better clamp meter from a neighbor and it reads way lower, so I think the cheap one was catching the compressor startup and skewing everthing. That matches what someone said about inrush messing with readings. Still bugging me though, since a couple of you said the heat element lets an overload ride for a while. How long is that window roughly, like minutes or hours?