I'm fairly new to logmein, but I had the same problem. I found that at some point my proxy on logmein was set on, when I was on a home network. I do often move to systems with and without a proxy, so I might have set it or it picked it up from my browser. I've not tried to repeat the problem yet. Obviously if you have the proxy set and don't use one or the otherway round logmein will show offline.