Theres nothing about recessive genes that make them inherently less likely or less desirable to pass on, and they're still there even if they aren't expressed.

If you imagine the genes as red and blue cards, red cards always go on top of blue cards. If you lay those out in every possible variation (RR, RB, BR, BB) the blue card is only ever visible in 1/4 of those combinations, the one with two blue cards. But there is an equal number of red and blue cards, if you shuffle them together and pick a card at random you have an equal chance (1/2) of drawing either color. So they don't die out, you just only actually see it 1/4 times