Our local auction site here in New Zealand, TradeMe, does that. Any bid in the last 2 minutes resets the clock to 2 minutes. Works pretty well for the seller, as prices tend to jump dramatically in these two minutes.

There is also at least one auction site with a similar business model that is practically a legal scam; bids cost money/points, and every bid increases the price by a fixed amount and extend the clock. Non-successful bids aren't paid back, of course.

There are actually some good arguments for a cost to bid system.

In theory it encourages people to bid their true preferences rather than waste time sniping.

Personally I find sniping quite enjoyable (as an idle-activity), but I also consider "recon" part of it (finding mislabelled or less widely known items that get the same job done usually results in huge effective discounts).