In my opinion, God being omnipotent, he CAN commit suicide, but the whole universe would return to the chaos at the same time.
And by the way, God is a very improbable being. If he exists, that means that the universe buts be larger than the big bang and eternal, which make unavoidable that God will appear again. It's a bit like rebooting an old computer with no hard disk. You loose everything and start over.
The idea is that we have a good idea that life is due to the fact that our universe favors continued complexification. On one side, we have natural selection which will favor everything that takes the place without killing its own sustaining environment. We usually consider this for living organisms, but it is also true for atoms : if energy creates particles, those which stable will survive and those which are not wont.
Now, about God, it's true that it's reputed eternal, but mathematics shows with the concept of ordinal numbers, that you can conceive numbers separated by infinity - and so, two point in time separated by eternity (which may sound strange - and I believe it's one limitation of modern physics : it implicitly excludes that kind of idea). This means that you could conceive God being eternal, but having a beginning which is infinitely far in time.
The problem with god, is that it should be a very complex being, and that, it is impossible (on a probabilistic point of view) that it would be there for no reason. however, if you have an infinite time, it would appear by complexification , and then have been there for an eternity - and for this reason, if he "killed" himself, it would necessarily appear again for the same reaons, in an infinite time.
Now, for this to be true, it would need that the universe is older that big bang, but this is not really a problem, because we cannot know if the big-bang didn't happen inside a larger universe.