This how Trade Me (NZ auction site) works: any bid in the last 2 minutes delays the close time to 2 minutes after the bid. That can happen repeatedly, and I've seen it go on for over 20 minutes on highly contended auctions. It works well.
If the winner, instead of paying what they bid, pays what the second-highest bidder bid (and bids are secret until someone exceeds them) then the incentives change. Everyone is incented to bid what it is worth to them, safely knowing (1) they won't pay more than that, (2) they will win the auction if no one outbids them, and (3) they won't pay more than necessary to win the auction.
eBay works this way (more-or-less), so you CAN (if you choose to) simply place your bid any time that is convenient and then ignore the timing of the end of the auction and all the sniping bots.