As a young man in the 50's and 60's the rumor was that he went to Argentina after the war .
Yeah, I remember those rumors. You still hear them floating around, every so often. Of course, we didn't know then what we know now.
Back in the 50's and 60's, there was at least the possibility that something along those lines could have happened. They might not have been the most plausible ideas, but there wasn't any truly definitive proof of Bormann's death (aside from Axeman's account, and he wasn't exactly the most reliable narrator).
But since then, things have changed. The body of Bormann was found, in a location which matches axeman's account, and it was forensicly identified as being Bormann, with DNA testing a few decades later confirming this. All the evidence points to the inescapable conclusion that Martin Bormann died on 1 May 1945.
Basically, those sorts of rumors persist today for two reasons. The first is that they became a small part of our collective memory of history. A lot of people heard that Bormann may have escaped Berlin, and not all of them are going to accept otherwise (or even learn otherwise). The second is that an escaping high-level nazi is perfect fodder for a conspiracy theory, either in and of itself or as a cog in a larger wheel. And, given that Bormann's true fate was only confirmed after the fact, it is a lot easier to insist that he survived than the idea that, say, Goring or Ribbentrop escaped.