That means the potential buyer has only 1 or 2 offers left that they can make. Unlike bidding, offers are limited to only 3.
As you probably know, you can reject any or all offers received. I've never used Best Offer but from what I gather from the Answer Centre, some people make low ball offers. Yesterday, a person made a $100 offer on an item the seller listed at $1,299. Some people think Best Offer is "name your price" and that they can get the item at whatever price they chose.
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Non payers should get unpaid item strikes and be added to block bidders lists. Period.