This just happened to me using the latest beta 4.9.4 -- Limewire dropped all four connections and refused to regenerate them. Every other network-using application continued to function normally -- web browser, etc -- and there had been no change to firewall/proxy/etc. settings (home broadband, so it wasn't someone else monkeying with the settings and disabling non-HTTP traffic or something). There is no proxy. There is a software firewall but it is instructed to leave limewire's traffic alone, and it hasn't been touched since when 4.9.4 was working normally. This has happened several times with all of the beta 4.9 series -- restarting Limewire seems to be the only recourse once this happens. Since restarting Limewire without touching anything else (firewall, rebooting Windows, whatnot) fixes the problem, it seems to be internal to Limewire.

Stderr console during one such incident with 4.9.4 shows a bunch of lines like this:
This is fairly serious since people having to constantly restart their clients is bad for the network, and likewise people being spuriously disconnected. Please have this fixed in 4.9.5.