I've had luck (not with Southwest) as long as I bought the ticket before it expired, I didn't have to use it by that day. Might be something to look into, but I'm sure Southwest is different than United.
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Bikes: 1996 Eddy Merckx Titanium EX, 1989/90 Colnago Super(issimo?) Piu(?), 1990 Concorde Aquila(hit by car while riding), others in build queue "when I get the time"