It sounds like either your isp or your modem/router. More likely the latter. See Connection problems? Check here first! & see how that affects you. May I ask who is your isp? May I ask what brand & model of modem &/ router do you have? What firewalls do you have? I'd be interested to know what your answer is to point #1 in the above link!?!

Don't forget also to try different options ... for a start, try deleting your LW Preferences folder whilst LW is closed; instructions here: Point #2 in Fixes for Limewire (sample image included.)