FWIW, we were rewriting a Visual Basic 6 application using web technologies. It's VERY hard for me to imagine saying "don't rewrite that VB6 application, just make it better". It's literally not even supported by Microsoft anymore, it was written by one person at the company who has since left, no one else here writes VB6, etc. etc. It was a critical business application, so it wasn't the kind of thing anyone wanted to just leave alone and keep on life support.
Even still, it's hard for me not to wonder if we did the right thing. Maybe we should have just hired a bunch of VB6 contractors to maintain the application and continue adding functionality to it. Maybe moving it to VB.net would have been better. Maybe there's some other migration path for VB6 applications...
Anyway, my biggest takeaway from all of this has been: think very very hard (and be honest with yourself) about how long a rewrite will take. Make sure "the business" and you are on the same page about how long that's going to take and making a serious commitment to focus on migrating to the new tool, and if you can, get it down in writing the conditions necessary to kill the old tool. If your users are anything like ours, they're going to have to be dragged kicking and screaming to the new tool, because we all hate change, so if you don't have clear conditions about when you're shutting the old stuff off etc. then it's going to be painful.