There are two ways to get to existing reservations at avis.com. Often for me one works and the other doesn't. The one that tends to work is to log in, and then hover over "Welcome, <my name>" and it shows my next upcoming reservation or two in a drop down (after a handful of seconds of a spinning icon)..

The non-drop-down method often doesn't work for me. (And since I never tend to have more than two upcoming reservations, the drop down method works fine enough for me.)