2009 Nissan Murano won't start, replaced battery 3 times?

My wife's 2009 Nissan Murano has some
type electrical problems. She has replaced
the battery three times, it may be fine for 2
or 3 months, then won't start. We can jump
start it, and it may be fine for a month, or 3
month's, and does the same thing. She had
the alternator tested, it was good. We don't
see anything left on that is draining the
battery. I'm not sure if it's related, but the
rear lift gate, which is power ( button)
activated, stopped working previously? Any
suggestions is greatly appreciated. Thank
you, John G.