Having AQ Vs. QQ and having a Q flop

What are the odds of this happening?

I was the guy who had the AQ, and I also had AK Vs. AA and an A
flopped. Happened to me in ring game play just today Online - I lost a nice chunk of money each time. Is this a rare happening?

It seems like it's a recipe for losing money if you are the one with the AQ or the AK...Is there a way to get away from these hands when this happens?
It seems to me like it's time to check-raise the flop and then at least call down with these holdings...

I would like to know how often this happens (to know if I should be paying attention to this while playing or if it's such a rare happening that I should not worry about it at all...).
It's tough to let go of an AK when you flop that A...

Thanks,