I've been hasted and invisible, crossed a transition line, auto-attacked the monster sitting on the other side of the transition, ran some distance with the monster chasing me, cast invisivility once I had gained enough ground, outdistanced the monsters so much I lost sight of them, stopped and they caught up with me.... I then recast haste and ran across three transitions (still invisible). Waited to be sure I was not being followed anymore, then still invisible went back to fin the monsters. They were right on the other side of the first transition I crossed and were still able to see me. So I don't buy the "hearing" Theory.
It has not happened to me often but It has happened more than once. I've been able to "escape" monsters by using invisibility a couple times when being chased but often I have to get out of visible range BEFORE I cast invisibility to get it to work.