This pair is odd because while they are technically singular and plural, respectively, "faculty" refers to more than one thing and "faculties" to one thing!
"Faculty" is the academic staff of a school or other institution. "Our faculty include a math department and six social science professors."
"Faculties" means "mental capacity," or "sanity." It is a good term to use to discuss the results of brain damage.
"Thomas Jefferson's daughter Polly caught typhoid in Paris, and it may have robbed her of some of her faculties; she was always quiet and slow after that."
"After the brain is deprived of oxygen for more than ten minutes, it is possible the patient could lose some of his or her faculties. We recommend occupational therapy."
"The students are so awful this year that half the faculty have lost their faculties!"
So if your university's adjuncts all quit, you have lost your faculty, not your faculties.(Please retain the reference in reprint: http://www.letpub.com/index.php?page=author_education_faculty_faculties)