Intermittent connectivity can be the sign of a faulty internet connection, limitations imposed by your ISP, or errors caused by any hardware/software applications connected with your internet connection, such as driver incompatibilities, old hardware, a slow/overloaded ISP or many other possibilities. Also, if you get disconnected from the Gnutella network, it will have no impact on your downloads already in progress. There is also a known issue that affects some Windows XP SP2 systems that causes LimeWire to disconnect and remain disconnected. To find out if it affects you, do the following at the moment LimeWire becomes disconnected:

Go to: Start > Settings > Control Panel (Make sure you are in "Classic" view)
Go to: Administrative Tools > Event Viewer
Click System in the list on the left side of the window
If you see an error with an event ID of 4226 that was generated at the moment LimeWire disconnected from the Gnutella network, then the following suggestions should help to reduce the occurrence of that error:

Open Limewire
Disable Ultrapeer Capabilities in Tools > Options > Speed
Minimize the number of simultaneous downloads (can also be found in Options > Downloads)
Minimize the number of other internet programs used alongside LimeWire
Restart limewire