I don't think that you will fold so many people with a 3bet on the flop for the same reason I wouldn't fold to a cap: that looks so incredibly stupid that I think it is worth one SB and a check/fold on the turn unless you plan to never steal again on that table. I know that image is not so important online, but folding to a cap after 3betting is something, everybody notices...
Maybe you should have tried a check-raise. That's a stronger move and doesn't look so weird if you fold to a 3bet.