Without knowing anything about your QT files, nobody can tell you much. This could simply be an issue with a specific CoDec or QT version. That said, there's nothing to fix. CS6 is done and sits on the "legacy" shelf and nobody will do anything with it ever again.
Yes, I can only assume that it is something wrong with my Quicktime files or at least that something in them is causing AdobeQT32Server.exe to throw an error that is not being handled. However, the point is that the AdobeQT32Server.exe file included with the more recent versions of AE doesn't throw this error. So there is something to fix. And I'm hoping that its isolated nature makes it relatively simple.
Now to the 'legacy' point. CS6 is still included in the Creative Cloud installer. And it does get updates from time to time. That's a good thing. Having a stable version of AE that doesn't require a subscription provides a much appreciated alternative to CC.
So, Adobe, if you are still updating CS6, please consider updating this .exe. I hope it's a simple one.
They haven't updated CS6 in years. The only updates it's getting are updates to the Camera RAW plugin which are being done by the camera RAW team and not the AE team.