Well, a lot of times the Hamachi server is horribly laggy. (The Hamachi server is used when you first start the connections to other users, it 'bootstraps' the connection so the connections will stay open even though you have NAT on a router). Some days it's better than others.
However it could also be the wireless issue. Sad to say, those types of setups (where you buy wireless net access from a server, there's one in my city too) can get bad because you're sharing a limited amount of bandwidth. So, if someone is using all the bandwidth by downloading a lot of files, your connection quality suffers, and that might be enough to break your connection to Hamachi.
When Hamachi stops working what about other apps, like downloaders and webbrowsers? do they seem less responsive or download stuff slower?