When your connection drops off, do you have files downloading?
And how many files are you sharing?

If you give us your system details, it'll help. For starters, we'll at least know which version of LW you're using Click on the blue link below & post the answers to those questions.
System details - help us to help you -> Provide these details when you post!!!

In the meantime - make sure that your Java's up to date. Java SE Downloads
Download the JRE offline installer & remove any other Java versions via Control Panel before installing another one. Reboot your computer after installing the new Java version.

Also try disabling performance options...
LW 4: Disable all options (TLS, DHT, UP capablilties) within LW's tools > options > advanced > performance. Click Apply > ok to save the change.

LW 5: In LW tools > options > advanced > super really advanced > performance. Disable ultrapeer capabilities, connecting to DHT & also TLS > ok.