Well, it doesn't actually work out exactly like this, but for giggles, let's kick the amp hours discussion around for fun.
2600 mAh = 2.6 amp hours. AKA. 2.6 hours of run time at 1 amp drain.
1.2 ohms at 3.7v is 3.1 amps. So that's 3.1 x the drain rate of the above. Or 2.6/3.1 = .8387 hours = 50 minutes. Optimal.
50 minutes X 60 seconds = 3000 seconds. 3000 seconds /600 hits = 5 second hits IF IT WAS NEW. (You could also say 1000 3 second hits, etc.) But it's used so even if you take 2 or 3 second hits, you may only get the 600 vs the 1000+ you got when it was new.
That's a real rough calc. And doesn't count how the cut-off voltage works vs optimal nor allow for the greater drain of high amp applications vs mA applications effect on the results, nor does it account for device efficiency losses.
So yeah, if you take 4 or 5 second hits, or even if the battery is older now, it's going to be lower.
That's to be expected. Sorry. But when these non-swappable battery power supplies get older, they don't last as long. Same is true for swappable cells too, but you replace them for 5 or 10 bucks in swappable battery units.
I can tell my 2 month old cells are not optimal anymore.
Basically, you're pushing a lot of amps/watts with those coils.
Best guess.
(someone check my math!)