Why is this seller asking for more money? The only justified reason that comes to mind is if it's a courier delivery to a remote area with a delivery surcharge.
Otherwise, your options are to ask them to cancel the order, or stick to your guns and to pay the price you won it for - you can then use eBay's money back guarantee if they don't deliver the item. It's a pain, but sellers who won't sell and buyers who won't pay are a perennial problem on eBay.
As regards being outbid at the last minute, it isn't the latest bid that wins, it's the highest. If you're bidding in the last few seconds there won't be time to increase your bid if you're outbid. You need to enter the maximum you would be willing to pay. That way you will either win the item, or lose fairly to someone who was prepared to pay more.
