The G20ei ignition module is well known for a very high (and, comparing to other ignition modules, unreasonanble) current consumption.
there arent many solutions - you can use a higher capacity battery, a 2500mAh will do the trick.
you can also change you ignition module to a differnt brand - like CH, their current consumption is approximately 350mA at WOT, your ignition draws more then 1200mA at WOT.
changing the ignition module requiers you to re-time the engine for a proper operation.

edit:
did some reading - it seems that the g20ei ignition module draws 1.6A for 4500rpm and up ... this is crazy...

found it here
http://www.toni-clark.com/ftp/ZG20_english.pdf