<p>I'm looking for a few talking points I could use to convince coworkers that it's NOT OK to run a 24/7 production application by simply opening Visual Studio and running the app in debug mode.</p>

<p>What's different about running a compiled console application vs. running that same app in debug mode? </p>

<p>Are there ever times when you would use the debugger in a live setting?  (live: meaning connected to customer facing databases)</p>

<p>Am I wrong in assuming that it's always a bad idea to run a live configuration via the debugger? </p>

I can't speak for everyone's experience, but for me Visual Studio crashes a lot. It not only crashes itself, but it crashes explorer. This is exacerbated by add-ons and plugins. I'm not sure if its ever been tested to run for 24/7 over days and days and days the same way the OS has.
Your essentially putting the running of your app at the mercy of this huge behemoth of a second app that sounds like its easily orders-of-magnitude larger and more complex than your app. Youre just going to get bug reports and most of them are going to involve visual studio crashing.
Also, are you paying for visual studio licenses for production machines?