If you replace rims when the track feels concave, you'll go through a lot of rims and spend a lot of time or money, though you'll be very safe. I let mine go until I feel throbbing in the brake lever, then I stop using that lever for the rest of the ride and replace the rim before riding that wheel again. Once I let a little air out of the tire because it seemed close.
It's also good to make a habit of pumping your tires at home before every ride, then spinning the wheel while watching the track. I've caught a couple of thin rims that way, too.
I wouldn't start a major brevet with bad tracks, though.