For any program that bases its requalification from January 1 through December 31 (and almost all of them do) the best time to get comped is in early January so you have the whole year to requalify. Most programs will only comp you once so you want to avoid a situation where you get comped too late in the year to permit you to requalify for the next year.
Personally, I would recommend extreme caution is requesting comp status because most programs will only do this once in a lifetime, or at least once in a long time.
Having said all that, I originally got comped to PremEx by UA in June and thought it would be a push to requalify. As it happened I flew about 70,000 during the remainder of that year, but I remember worrying about it for a while.
Good luck.