You cannot suppress AppDomain.UnhandledException. Something really nasty happened, a thread in your program died from a heart attack. The odds that the program will continue to run in a meaningful way are zero, .NET puts an end to the misery by terminating the program.
Write an event handler for the AppDomain.CurrentDomain.UnhandledException event and log or display the value of e.ExceptionObject.ToString() so you know what caused the mishap. That gives you a hint how to fix your code. If any, it may well be something that you cannot fix yourself. Some kind of database server malfunction for example. Doing anything to intentionally hide the error is therefore a Very Bad Idea. Your customer's support staff will have no idea what to do.