We're flying IAD -> DEN -> SUN to see the eclipse.
We have a 37 minute connection time which I started to worry about.
I called United to change IAD -> DEN to a 2 hour earlier flight.
Although there are plenty of seats on that, the customer rep. said she couldn't change us to that because DEN -> SUN has a waiting list. She said to change the first flight she'd have to take us off the second flight briefly, and in that time our seats would go to somebody else!

This seems rather bizarre to me - is it really the case?
If I tried a different day with a different rep. is there any chance of getting a different result?
The rep. suggested that possibly there was a problem because I'd bought the two flights together from a travel agent (in this case orbitz).

Thanks!