Dunno about the Zoom G series, but I have a Zoom 707II up for sale which ONLY works on 1000mA adapters. I don't know why this happens but it happens. Another guy had the same problem with Zoom707II and when I advised him to fire up through a 1000mA adapter, it worked.
I don't know why it happens, since the proc rated amperage is 300mA. I wouldn't suggest that to you for fear of frying the proc. But yeah, this happens.
@amit25 : I tried upping the voltage and that didn't work with mine.
My gear, currently up for sale
Washburn X-16 anarchy - SOLD!!
duncan pickups - I wonder why Im selling these.