When this takes place, is the entire electrical system failing / shutting down? Is it a defined, hard click, like from the starter, or a soft click, like from the starter relay? The starter relay has been known to fail on these vehicles. I'm not saying go out and buy one and hope for the best. I'd investigate a little more before I went out and dropped money on a part on a hope.
White 2014 GT coupe / Auto Trans / Louisiana