I already tried re-seating the wi-fi card and antennas. This problem seems to have something to do with the computer getting "warmed up" and then losing the connection. Maybe at home I can get it to happen reliably enough to convince Dell warranty support to attempt a fix. The problem I see is that it could be the wi-fi card, but could also be the antenna wires into the laptop's screen. Phooey.
[Composed offline in Columbus Airport; posted after getting home.]