How is it possible to close ArcMap when your form is modal. I think your forms are non-modal. Maybe it's a solution for your extension. Put your form as modal. With this, users must close this form before close ArcMap.
But I think it's not what you want, it's just another way.
Maybe you have a connection problem in your forms. which kind of connection you have in your forms (Oracle, PGDB, FGDB others..). That could be another problem.