That host potentially can support long duty cycles, it looks substatial. I would still stick to 2 minutes and less. A true 880ma 16340 battery will give about an hour at 1W. If the battery is dead, from a full charge, after running ~1amp for 3 minutes, then you have a bad battery. If the laser works fine again after it rests for a while/ cools down, shorten your duty cycle (on time) as something is probably heating up,the driver possibly.
No way - not a chance. For one, there's no hope in hell that they gave him a true 880mA 16340 battery as the freebie with his laser purchase. Plus, 880mAh wouldn't come anywhere close to an hour of 1W runtime. For one, these Chinese builds aren't running the latest M140 higher efficiency diodes. Two, their lenses aren't anywhere near as decent as a G1 or often even a 3-element Aixiz. Three, they're using a boost driver, which not only means a higher current drain on the cell, but also implies efficiency losses. To get 1W, you're probably looking at more like 20 minutes from the CR123 cell. Now, granted, the one thing that works in hist favor, is that this probably isn't a true 1W laser either
But, there's no real mystery here. The operation sheet was written by liars.
1) Your CR123 is probably 600mAh in actual capacity.
2) Your laser's diode needs ~5V, and maybe ~1.2A to deliver ~1W of output.
3) Your battery supplies a nominal ~3.7V
4) The boost driver in that host is maybe 80% efficient
5) That implies a current draw from the cell of ((5 / 3.7) / 0.8) * 1.2 = ~2,025mA
6) At 2,025mA of currect draw, your 600mAh cell should be depleted in ((600 / 2025) * 60) = 17.7 minutes
In other words, they were stupid for suggesting that you'd see 2 hours of run-time. 17 minutes is more likely. If you're seeing it dim after 3 or 4 minutes, then it's probably a combination of crappy diode heatsinking, crappy boost driver heatsinking, and a crappy cell.