Don, when you had that meeting, did anybody make a list of which channel number each neighbor is using? Your Wi-Fi system can operate on any of 11 different (but overlapping) channels, and if several nearby systems use the same channel, the signals will interfere with one another.

And because Wi-Fi uses unregulated radio frequencies, it's possible that smebody in the building has a wireless telephone or a microwave oven (or something more exotic) that is knocking out your signal under certain conditions.

Either way, you might solve the problem by changing your base station to a different channel. I've forgotten what kind of base station you have, but it's easy enough to change the channel (easy for me to say, right?).

I think I gave you a copy of my book, "The Book of Wi-Fi," that explains how channel numbers work. I can probably talk you through changing the router's channel number by telephone.