The auction needs to be started by the deadline, so bidding can drag on into the playoffs a bit.
But, you reminded me of a subsequent rule that I usually announce along with this:
You cannot bid on a player after the deadline if you had no other bids in that auction prior to the deadline. This means if Team A and Team B are in a bidding war for a player that extends until after the deadline has passed, Team C cannot jump in on the bidding if he wasn't in on the bidding previous to the deadline.
This prevents someone who maybe gets an injury on Monday or Tuesday and throws up a bid on an existing auction since that's the only player available to acquire, screwing over the team that made the original pre-deadline bid.
Does this make sense?