Clearing your browser cache.

Tools > Clear Recent History... - hit Details and make sure only Cache is selected, then select Everything and hit the Clear Now button.

While admittedly I'm not offering a solution to this problem (I have the same one and I came here seeking a solution), I have to immediately criticize the last "solution" offered. The original poster asked how to fix a problem with HP Support Assistant giving a fail message when it attempted to clean the Mozilla Firefox temporary internet file folder. The only person respond explained only how to manually do what what the problem software was supposed to do. The original poster asked how to fix that particular software, not how to do what that software is supposed to be doing automatically. PLEASE read the question people.

Why not ask HP support about their software?