If you're airing them up every few days, to a normal road bike pressure range, and the tires are completely flat no that is not normal. Either something in the tire or wheel is pricking a tiny hole, or you or your pump are doing something to the valve stem.

First thing I'd check is the rim tape, replace if it's the thin rubber type that comes stock on some wheels. Check the tubes again, get out the magnifying glasses and cotton to check the tires.

I haven't replaced tubes in our two mountain bikes, ever. My road bikes, which I ride one or the other daily, haven't seen a new tube in a couple of years. Normal air loss on my road bikes, they won't be flat until months have passed.