Ok I see, I'll give that a go!
So just to clarify, so the battery is slowly discharging which = a weaker and weaker spark. Changing the spark plugs helped this at first because the other ones were sooty (probably from a weak spark?), so improved the spark. But when I changed them after running it for a while it didn't help as the plugs were ok and the discharged battery was still causing a weak spark.
I don't understand why though after it running and dying, then letting it sit made it run ok for a while. I thought the battery would not have changed voltage thus = same weak spark. Although, after it died and letting it sit, I gave it more throttle and was keeping the idle higher when stopped, so was it just the high rpm that kept it alive? edit: yes I think it was