Hmmm. Dont have much experience with beeping sounds, id bet some of the other experienced members here have a definitive answer for you.
My guess, its overheating..... Video cards are pretty straight forward. They either work or dont work, only fan speed or heat is going to cause them to malfunction....just by basic logic. Maybe power related?
Did you bother to check your temps when it makes this sound? And are you positive its actually the video card beeping? Hopefully its not some insufficient power related issue.