Odd problem. I can say your ISP is known to shape or block LW, but not in all their regions. They seem to have different attitudes & approaches in different areas. That in itself may result in inconsistent speeds. To start off fine but then drop to zero. But if hovering your cursor over something fixes it then the problem sounds like something else.

To me it sounds like a java issue. So removing all versions of Java & reinstalling using ONLY the 'Offline' installer seems a good idea. Also, make a note of all your options settings & then delete your LW Preferences folder whilst LW is closed; instructions here: Point #2 & 3 in Fixes for Limewire (sample image included at bottom of page.) But be sure to reset everything back to how it was before next time you open LW. When you open LW again, you will need to reset all options. So to reiterate, make a note of all settings under Tools>Options>...