Hi Guys,
Are you still seeing this issue with the most up to date version?
Which is Version 2.2.0.410, available here:
https://secure.logmein.com/hamachi.msi?_ga=1.165689657.665825872.1448362914
If you try uninstalling, reboot, then reinstaling with this link, does that help?
(make sure to reboot after the uninstall to clear out any trace of the app)
If not, can you try running the new diagnostic tool under 'help' and seeing if that points you towards what is causing the app to go offline!
Cheers,
Colm