Once a case has been resolved, can the plaintiff go back and re-file a claim on the same issues?

Your brother can sue, because anyone can sue for anything, but whether you can get his case dismissed based on the prior ruling depends on two things.  First, was his earlier case dismissed on the merits?  If it was dismissed because, for example, the Court held that the statute of limitations had passed on his claims, that would be on the merits.  If it was dismissed, for example, because the Court held that he had not properly served you, that would not be on the merits, and he could sue again.  Second, assuming that his earlier case was not dismissed on the merits, has the statute of limitations has run out in the interim since the first case was dismissed.