I did a quick scan of his Wikipedia page and here's what I found:
Apparently when the multiverse was recreated after Infinite Crisis, he was reborn along with it. I have no idea how as that doesn't really make much sense, but that's what happened.
Then Superboy Prime killed him in The Sinestro Corps War.
He was in Blackest Night, but since he was essentially a Zombie I'm not counting that.
He was then resurrected again in Brightest Day.
Then The New 52 happened so none of that really mattered because a new version of the Anti-Monitor was introduced along with the new continuity.
Then Death Metal happened and it's revealed that Perpetua is his mother (WTF?) and then something happens and he gets reverted back to his original appearance.
But then since Death Metal made everything that happened in history canon, all the stuff I wrote before The New 52 apparently
did count somehow.
So as you can see, it's a very simple answer. Just like most of DC's continuity