I was watching the timing carefully.
I know my wife was already scanned, because she called from the plane.
When the flight status said "taxiing to runway", I tried again. Nope.
About three minutes later I was able to check her in.
There must be some sort of "close out" process that the gate agent does after the plane leaves that changes the status of the reservation from "checked in" to waiting for next flight segment and available for new checkin.
Of course, by then she was number 10 to check in, rather than lower. Since she is gold, that could make a big difference in her battlefield upgrade this afternoon.
Thanks for all the replies, next time I will try the hint about not logging in.