it seems there are two separate kinds of problems:

1) limewire can't establish connections to hosts right away. in the 'connections' tab, there's a whole bunch of hosts either 'connecting' or 'handshaking'. in this case, limewire should eventually establish a connection and the dot should turn green.

2) brief green dot, then red again, and nothing happening in the 'connections' window. there may be more than one reason for this but it definitely happens when you're not connected to the internet. i am suspecting that some users who connect to the internet through a modem open limewire before they're dialled in. but there may be other reasons, too