Hi Wendy - We don't have quite enough information in that we don't know what the buyers' objections were. I would expect the unpermitted space to be an issue if it creates a "non-conforming" space. It could be non-conforming if the unpermitted space doesn't meet setbacks, for example. This would show up during a mortgage survey and create an issue for lenders. Some homes have an "illegal" apartment. Such a space, obviously, should be marketed as an in law suite, not a duplex.
Without further info, here is my suggestion: The Seller's should consider permitting the space after the fact. I have seen this done. The people involved had to bring the unpermitted space up to code, but they were eventually issued an occupancy permit for the unpermitted space.
Some mitigating issues: If it was done by a previous owner, sometimes the space can be "grandfathered". Some code officers would be more understanding of a homeowner who just didn't know any better than a builder who just broke the rules. If it is non-conforming, sometimes an appeals board will approve an exception, esp. for senior citizens.
Worth a look.