1999 Tahoe with sporadic failure to start

My 1999 Chevy Tahoe (86,000 miles & well cared-for) has had a frustrating problem for years: it occasionally won’t start. It will sound like it’s trying, but it just won’t start. This always happens when the engine’s cold. It alwyas starts eventually, 30 minutes to several hours later. We wondered if it might happen after a lot of moisture, as it seems to have happened mostly after hurricanes and rain storms, although sometimes it was preceded by no rain at all. I tried looking up the problem online, and found discussion boards where other Tahoe owners had the same problem - but no explanation or solutions. A full tune-up was done. My daughter is tired of being late for school and I do not wish to be stuck at a roadside motel in the Everglades again. Anyone heard of this problem and have some useful advice?

Problems with moisture when starting is usually solved by a new set of plug wires.

Thank you, but as I said, a complete tune-up was done, which included new plugs & wires.