In case anyone still needed a solution to this Issue, I found that simply disabling the DTI preference in Server Configuration > General > Windchill Overlay Icons in Windows Explorer (Like Stephen mentioned earlier) stops Windows Explorer Closing.
This is not really a fix but is a solution, As long as the preference isn't enabled then WE is fine
I submitted this same problem to PTC in June 2014. They still have not figured out what is wrong (as of Jan 2015). There seems to be a wide variety of errors here from none (works perfectly) all the way to cannot even install DTI. Please keep this thread going.
Glad to see I'm not the only one to have this issue. PTC cannot replicate and has closed the case for now. They gave us some more logging to enable but we haven't had a chance to try it yet
Please enable the user-mode local dump to generate full crash dump whenever explorer crashes and send the dump for analysis. Please refer below articles to configure the local dump. Basically you just need to add few registry entries.
I had problems with Windows Explorer closing unexpectedly for a long time on my machine. I found it was caused by the many, many different versions of Windchill DTI that had been installed over the years. I tried lots of ways to fix things, but ultimately, it was a full un-install, followed by a Windows registry cleaning of all DTI keys and a new installation that cured it. I have not had a Windows Explorer problem in a long time.
Please keep working with PTC Technical Support. They are here to help and should be able to resolve this issue for you. The more ways you can isolate the issue, the easier it will be for them to diagnose and find the root cause.
I don't think I have had even one Windows Explorer crash, since I made the configuration setting change that Stephen O. recommended on Server Configuration > General > Windchill Overlay Icons in Windows Explorer.
If you know of a fix coming from PTC, would love to hear about it. The overlay is not critical by any means, but it is a nice feature.