2003 Eclipse GT automatic

This all started in March after my battery died. I had my car jumped
and on the way home I had to keep the idle above 600 or it would stall.
I got a new battery and ground cable from checker auto parts. The
problem continued so I took it to a mechanic. He noticed that a plastic
piece on my air intake was broken, so he replaced it and everything was
fine. Well a few days ago, my battery died again. I had it jumped and
the problem started again. My car idles fine when cool, but once it
warms up the idle drops to 0 and stalls. Sometimes it will idle fine if
the AC is on, but once I turn off the AC it stalls and sometimes the
idle goes up and down but doesn't stall.  I took it to the same
mechanic and he looked at the intake but it was fine. He suggested I
take ut to a Mitsubishi dealer. The Mitsu repair man told me I had to
buy the stock ground harness before he tries anything else because I
may not be getting a good enough ground with the aftermarket ground I
have. He wanted to charge me $382 for the harness plus labor, so I said
no. Any ideas?