Betting out of position: when to give up?

[Pokey]

Frequently, I find m'self called by the CO or Button when I raise first-in with something nice like AQ or AK. Then, the flop comes -- blank. I bet it, the cold-caller calls again. Turn blanks again. I bet again, the cold-caller calls again. River blanks me a third time. At this point, I'm usually at a loss for what to do next. Do I throw another BB at an increasingly unlikely steal? Do I continue to vomit chips into a pot where pocket 2s or a stray bottom pair beats me?

The situation I'm describing is this one:

1. Heads-up
2. Overcards only
3. Useless board
4. Passive opponent who calls to the river

Do you keep up the fire? Do you give up and check on the river? On the turn? Do you even bother to bet the flop?

I consider this a huge leak of mine, and I'm not sure what the best way to fix it is. Any advice would be appreciated.

[Harv72b]

Generally, I'll bet the turn & check through the river. But it really depends on your read (if any) on the opponent. Against an aggressive opponent, I might check through on the turn & call a river bet. Against a loose/passive who'll call down with A high, I'll bet the river. Against a tight, solid player I'll check through the turn & fold to a river bet (unless it was a really drawy board). Against any opponent, I'll vary my play from time to time anyway.

Then again, this is an area of my game that I'm not all that happy with, so there's probably a better way of conducting business.