old schoold debugging...but still the best i think. Why not write your own quick logger...add a log entry at the beginning and end of each of the most widely called procedures. this could help in identifying some pattern in the randomness...if there is any...
i don't think that would take too long. basically you could create a global reference to a log object that can be referenced from any page. that can be stored in a session or server variable. doing that you can simply add log entries where every you choose quickly and easily.