When you are running as a leaf, 3 connefctions is what it should be, more won't drastically improve your search results, but will waste bandwidth.

On the other hand, for this to work, you should have stable connections. If you have a router, try setting it to forward port 6346 to the local IP address of the machine you're running limewire on.

generally, it may take a while for limewire to find good hosts to connect to. it seems that it quickly drops connections to non-limewire hosts.