When a system is behind a firewall and network address translation, Hamachi performance of using UDP and direct tunnel mode is very dependent on how the firewall handles the NAT especially for UDP.
On some firewalls there are options under advanced settings or VOIP settings to enable "consistent nat" or other settings to better enhance the NAT'ing of UDP typically for VOIP phones. Enabling consistent NAT may help in establishing and keeping direct tunnel mode.
If not, then you will need to statically NAT TCP and UDP ports for Hamachi. Of course if you do not have access to your firewall then that would be a problem. Here is a video on how to statically NAT for Hamachi.