To see if we can work out if the problem is what I suspect it is, try something for me. Go to Utilities folder, open up Activity Monitor. Keep a pen & paper handy. Then open up LW, make a note of how much RAM, CPU & especially VM (virtual memory) that LW uses. Make recordings every 5-10 mins. Do a search & see if the VM amount increases notably directly after this. And keep making recordings up until you lose connection.

BTW does LW crash at all? If yes, post segments of the crash report. (You'll find crash reports under -> OSX HDD >Username>Library>Logs>Crash reports)

(BTW see my pm (personal message in your user cp)