We already discussed this for a while in another thread some time ago. I proposed the same exact thing that Yarden is proposing (and I never even played or knew anything about sokker).
Anyway, my patch to this problem is to bookmark the guy I'm bidding on. Keeping a tab open on the guy and refreshing works well for the last minutes of the auction.
but yes, if the Bids page could keep the info about a player we had a bid on until his auction is over, would be great. (Like the list of players your are involved in the auction of).