This is how the popular car auction site bringatrailer.com bidding process works for cars sold on their site too, a quirk of which is that it makes watching the end of the auctions live online kinda fun, especially given the discussions that break out in comment section on each car up for sale while folks nervously watch the current candidate for the final bid cool down.
Much like your example, in the two minutes before the end of the auction, every new bid placed extends the auction clock by another two minutes, the winner hasn't won the auction until two minutes have passed with no further counter bids.
Auction site design where most every transaction is a very material amount of money for buyer and seller probably have different trade-offs from something like eBay where most items are rounding errors compared to the income or wealth of the participants.
For example, think about "sniping" from the seller side. Sellers are rightly concerned about any wrinkle of the bidding process that might leave money on the table. Automatically extending the time so that every potential buyer has time to "answer" a new bid soothes the concern that buyers were willing to pay higher, but they didn't have the technological prowess to post their bid in the last 0.3 seconds.
With ubid, you also had the feature of letting it bid to your highest price. Yet they still extended the auction if someone outbid your highest price.