Hamachi VPNs are picky about their connections and need a constant, strong connection to maintain the VPN link.
I'd run a long ping against an outside server or from instance to instance and make sure there are no fluctuations in the packets going through.
If you're running wirelessly I would try a wired connection as I've had problems with the hamachi Von cutting out on wifi when gaming but being more stable on a wired link.
Finally, check the network settings within the virtual machines and possibly tweak or disable the firewalls or antivirus in the virtual machines since their routing or scanning could be slowing the network and causing the disconnects.