I also get the 'no internet connection', but I'm still on 4.9.17. Sometimes even when downloading, but most of the time it's while starintg/connecting to the first ultrapeer.
(while downloading means: it's downloading, but is connected to 0 ultrapeers)

What seems to happen is that limewire tries to contact ultrapeers from whatever list it has/keeps/gets/whatever and goes through all of them, connecting to none. Then it reports no the 'internet connection' dialog. I can't tell which one of the above it is, I hope you can find out from this info.

This has been happening a lot, and seems version independant (it is why I updated from 4.8.x to 4.9.17 in the first place). It also feels like a bug more than network conditions, since it happens so much. But that isn't consistent with the fact that it started happening in 4.8.x out of the blue. A bug in other ultrapeers? (Or are some ultrapeers refusing Limewire, and are users accidentally hitting only those? Too much of a conspiracy theory I guess.)

But what then? I'm not sure... some more facts: it stops randomly as well. It happened on startup just now, I reselected file/connect, and saw it go through a million non-connectiong ones again, but it found some in the end apparently, as it's working fine now. 3 ultrapeers, 2 4.8.1 and 1 4.9.1 limewire.

hope this may help... (about to install the beta)