I used to think that I had the same problem: Limewire (or other p2p apps such as BitTorrent) crashed my connection at seeminlgy random times.
Well, I've figured out my 'problem'. Turns out my stupid ISP automatically shuts off connections that are active for a precise 24 hours. Can you believe it? Why would they do that. To my knowledge, no other ISP (at least in France) does this and mine happens to be one of the most expensive, if not the most expensive of them all. You'd figure that with the money they take from us they wouldn't do that to us.

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iMac G4 OSX 10.3.9
RAM 256MB
LW 4.10.5 Basic
ADSL anything from 3 to 8Mbps/around 1024kbps

"Raise your can of Beer on high
And seal your fate forever
Our best years have passed us by
The Golden Age Of Leather"
-Blue Öyster Cult-