I've learned my lesson. After buying, and replacing, a bunch of cheapo keyboards, I bought a good wireless keyboard (on sale, of course). It finally gave up the ghost - but it lasted at least 5x as long as any of the cheapos.
We're currently using a cheapo that was still hanging around the house while I watch the flyers for a new wireless keyboard. After very little use, one of the keys (backspace) has already committed suicide.