Yep, stand your ground. Make sure in your negotiations that he does not re-create history so it looks like you knew something on the compliance concerns prior to the sale.
It is unclear whether you have closed the sale (and the buyer is having "buyer's remorse) or you have yet to close and you are negotiating certain issues to get it closed. If you have not closed, I suggest you get an attorney ASAP. I would be happy to speak with you on this matter.
Otherwise, assuming you have closed, a well written PSA should have a limits to your liability and the amounts for which you may have to indemnify (i.e., reimburse) the buyer post-closing. Additionally, you have to review the representations and warranties you made about your business. So, even if the buyer has a legitimate complaint, depending on what your PSA states, the buyer may be out of luck.
In Illinois, generally speaking, if your PSA does not contain both
an integration clause (i.e., this PSA reflects the entire agreement between the parties), and
a "reliance" clause (i.e., neither party may rely on any representations, warranties, etc that are not expressly stated in the PSA)
then your buyer will have a very difficult time in bringing up issues outside of the PSA.
This answer is for informational purposes only and is not intended to be legal advice nor does it establish an attorney-client relationship. You should consult a local business lawyer to obtain legal advice that is tailored to your circumstances and facts. Good luck to you.
Just a correction of a typo in Mr. Flemenbaum's thoughtful answer.
When he wrote: "In Illinois, generally speaking, if your PSA does not contain" he meant "if your PSA does contain." I think he began the sentence to warn you of the danger of the absence of these clauses, and ended it explaining the benefit that such clauses would give you.