Do you use the Resume/Find Sources function on many files? If you use it on too many files simultaneously, then on some people's systems it can use up not only LW's resources but also your computers resources. Thus your computer will stop communicating with your modem/router. After opening LW, let it settle for 10-20 mins before using. If you have many shares & many incompletes then perhaps even a little longer. This varies depending on system, etc. "If" you're going to use the Resume/Find resources function, then apply it to just 1-3 at a time. You might also want to consider reducing both downld & upload bandwidths slightly. Also, set both your uplds & downlds for auto-clear. Also, tick the option under Speed for Disable Ultrapeer Capabilities off. Unless you use iTunes, turn off iTunes sharing option.
You might also want to consider deleting your LW preferences whilst LW is closed. But make a note of all your settings because once you do this, you'll need to reset all your options. See points #2 & 3 here:
Fixes for Limewire