Again, no "starting" battery can handle repeated discharges, AGM or otherwise. If there is a slow drain and repeated discharges, one needs a deep cycle battery.
While I have not experimented with slow draw on an AGM vs. wet acid starting batteries (cuz they aren't made for that), I lived in the mountains for 19 years (read: cold), in typical use (NOT constant draw however), AGM's typically lasted 3-5 times longer than wet acid batteries. In fact I found they were better in every way even with occasional discharge where they always recovered better than a wet acid.
In my old off-road truck, I had a dual battery setup. One Optima Red Top for regular starting/operating duties and one Optima Blue Top (Deep Cycle) for an electric cooler and air compressor. I basically drained that battery every night (on multiday, off-road excursions) running the cooler and I did this many, many times and it lasted me a long time. But, it survived this treatment.....because it was a deep cycle, the fact that it was an AGM, made it a better deep cycle.
I'm not sure why our results differ, but this is the first I've heard anyone state what you've experienced.