Most state nonprofit corporation statutes prohibit the expulsion of a member without a right to be heard at some type of fair hearing (except perhaps for failure to pay dues, in which case a hearing may not be required).  There normally is no right of further appeal within the organization so long as there was notice and the opportunity to be heard.  Appeals to court are not usually successful if the procedure, or the opportunity to participate in a procedure, was reasonable.  The statute of limitations on such appeals to court is often relatively short.

Having said all of that, I don’t see why you would bother with an appeal in this situation.  If you think he should be readmitted as a member, unless you have rules that prohibit it, you could just reinstate him to his prior status.  If that doesn’t work, he could reapply the way any other new member would apply and get admitted in the same procedure.
  
If you want him back, I am sure you can find a way to do it.  If you don’t, he probably waited too long to complain effectively.