From looking at the code you just posted I am guessing you were working with the floated parent version. IE8 is fine with that as we concluded in the thread I linked to. It is Opera 10 that is having problems with both of the test cases.
I just downloaded Opera 9.64 to make sure I was not loosing my mind since I did not recall any problems in the past.
Sure enough Opera 9.64 is just fine with both of those test cases.
The problem is not the overflow:auto on the fixed div. The problem is that Opera 10 is not keeping it positioned at bottom:50px; at all times. The background color is set on the fixed sidebar to show top:100px (header) and bottom:50px; (footer).
I did not see any effect that your inner AP div with overflow:auto; had on the positioning of the fixed element in Opera 10.
After testing in Opera 9.64 I have confirmed that a page redraw is not needed to keep the fixed div at bottom:50px;
I updated the test cases with footers just to make it clear what the 50px was for.