Can the FAA stop the municipality owned airport from closing down?
Frequently, municipal airports are created and/or operated with funds granted by the Federal Government that contain contractual obligations that the airport remain operating until a particular date or certain conditions.

I don't know about that particular airport.

Even if a municipality owns the airport free-and-clear without contractual obligations to operate it, the FAA does have a lengthy process for shutting down an airport.

Since you're in Wheeling, you may be familiar with Meigs Field, which was abruptly closed against FAA rules, leaving airplanes stranded, charts incorrect, and airplanes attempting to land at an airport that didn't even have a functional runway anymore!