We (ok, Craig) figured out why @partych.at bots were not accepting new invites -- basically we'd hit the number of un-answered invites the jabber server could buffer. Clearing this buffer appears to have fixed the invite issue.
This is probably unrelated to the dropped messages issue. I did upgrade the PartyChat server from Smack 3.0.1 to 3.1.0 last night which can only help.
If you're still seeing offline issues or dropped messages, keep letting us know (via comments on this blog is good) and we'll keep poking around till we get this thing fixed.
Update: partych.at bots may appear offline for you. This is because the partych.at XMPP server's roster database (i.e. who is friends with who) is now out-of-sync with your chat client. If you're using something like Pidgin, you can "unsubscribe" and then "re-request authorization" to the bot. If you're in a GMail based client, we're still trying to figure out how to do it.
Update 2: If you're using gmail chat (or something similar) go to the "Add Contact" dialogue and re-enter the partych.at addresses you were using. This will cause them to re-appear as online to you.