What version of Maya are you using? deleting the history is super important but do Make sur to download the Hot fixes and service packs. I was having the same error in my maya 2015 scenes just opening and switching scenes so I thought maybe my scenes were corrupted. Turns out it was just a bug in the system and the service…
Beveling that edge works for me on Maya 2013. However, your geo is not good around the corner points of those dense bevels all over your mesh. You have ngons and holes. Your Outliner (which I suggest you have open while working) is cluttered with many empty groups and dead transform nodes. I suspect these to be the cause…