I'd say if that's all the contract says, you have a very poorly written
contract. The contract should say that the buyer has the right to an
inspection, that it must be done withing a certain timeframe, that the
seller must be furnished a copy, what happens if defects are found,
etc. And it should also say that if the inspection is not done in
that time period, then the inspection contigency is waived and the sale
proceeds.

Did you have an attorney review this contract? I'd say if that's all
you have, then the issue is definitely arguable. Who drafted the
contract? Normally, a court would view ambiguities in favor of the
party that did not write it.