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Was this your first offer? Make another offer a bit higher (high enough to be a serious new offer, but not too high) but expect it to get rejected, then come up again to an amount lower than asking price based on what you think the vendor might stomach losing out on.
Reasoning: By this point you've made 3 offers and offered more each time. By the time you've made the 3rd offer you're going to be losing patience with them and potentially looking elsewhere so the vendor might be more likely to think you're a good bet and accept your offer. Also they will feel like they have negotiated well but making you offer more (two times no less!) and feel better about losing out on the asking price offer you were never going to make.
Argh, they want asking price, i went in £25K less...
What would you do?