The offering of upgrades, in my experience, is quite hit and miss and it doesn't always reflect what is actually available if you call up.

For example, if you upgrade one leg with miles, paid upgrade options tend to disappear from the remaining leg even when they remain available (although I think the auction remains visible, if offered).

Best plan is to call and speak to the Upper Class team, who are generally very good.

Incidentally, I don't think the auction is available on all flights -- but it can be offered from PE to UC.