Do you have many downloadtasks in the downloadwindow at the same time ??

That can be a reason. Limewire is trying to start them all, thus sending a lot of requests out. Your router may not be able to or is set to not handle that many connections at the same time.

If this is the reason then go to :

Tools>options>Speed and check the "Disable UltraPeer Capabilities"

Then Downloads. Set the number for simultaneous downloads low e.g. 4

Then Connections. Uncheck the box "Connect On Startup"

Press Apply then OK

Now you can connect after Limewire has loaded and it won't have as many simultaneous connections