Look at it from the offeror's point of view.
They've seen a house and are prepared to buy it at the asking price. They've found themselves, probably as a result of being scmoozed by some oily estate agent, bidding over that price.
Now the bloody vendor won't sell - at a price higher than they were looking for originally.
No wonder they're likely to withdraw their offer.
You've been bustled by your estate agent, who wants an easy sale and doesn't care about the marginal commission on 5 or 10 grand, into setting an asking price below what you want. This is an asking, not a guide, price. Buyers know the difference between the two and, while they don't expect to land a house at the guide price in the current market, they do feel that offering the asking price should get them the house.
If you have a higher price than your asking price in mind (and evidently you do) then raise the asking price. Don't get caught up in playing games with househunters with your estate agent.
Otherwise, do what your agent probably wanted you to do in the first place - take the quick sale.