Hi, do you have both versions (7.0 and 7.1) on the same computer?
There are not a known issues on "LV hang on exit", so I strongly believe it is related to your machine.
Even if it is not supported, I run many version of LV (including 7.0 and 7.1) on the same PC without any problem, but it not trivial setting up such a machine.
Hope this helps.
Regards
NicolaC
National Instruments.