Not so - if the purchaser is informed that the deposit is non-refundable it is their decision whether or not they wish to pay it over or not at the outset.
In the experience I outlined above, the "purchasers" were not in a chain, instead they prevaricated because of problems with their finances. Never again would I entertain a purchaser who does not have their finances in order, hence my advice to the original poster to assess the situation, back out if they feel that is necessary, and secure a non-refundable booking deposit in future.