One thing to keep in mind when using coin cells...
They may be rated at 200mah (give or take), but that's at a very low current draw, say 50uA. If you pulse it at 600uA, that 200mah battery will most likely act more like it's only a 50mah battery.
In other words, 10 seconds of 600uA is a lot more drain than 100 seconds of 60uA, and that's a lot more than 1000 seconds at 6uA.

Don't ask me why, it just the way it is