Continuation Bet after missing flop..Am I folding too much at river?

I recently made a very large stat post which turned in to quite a discussion. I'm still breaking even at a combination of 1/2 and 2/4 and one of the main things that got pointed out was how often I folded to a River bet. I'm currently sitting at like 59% fold to a river bet.

After thinking about my play, here is a common situation I run in to:

I get dealt KQ in middle position. I raise preflop and get two callers.

Flop is 10 6 2 rainbow.

I bet, one folds, and another calls.

Turn is a blank. I check, opponent checks.

River is another blank. I check with my unimproved hand, Opponent bets, I fold.

How am I supposed to play this differently? I find that if I bet the turn, my opponents calls anyways. Then they just call down the river and show me bottom pair to win the hand.

I understand that maybe i should call down more often if I had AK for example, but still..especially playing in lower limits, people will just continue to call my bets down and show me middle or bottom pair against my unimproved AK.

Any thoughts?