It's not a Facebook issue. They have made changes to the system. A Facebook Chat client is useless if it does not also support pushing Offline Messages because of the Nature of the Service. This is why Facebook also released the Facebook Messenger App on iOS/Android/BB.
Too many people use Facebook primarily through a Browser and Facebook Messages Agregates both FB Chat and FB Offline Messages into a single User Interface on the website. When they get your Chat Message - in Facebook Messages interface - and reply to it, their reply is via a Message, not an IM. That is why you do not get a PUSH notification from the Chat Client, but from the Facebook App. ((This is part of the reason some of us have always said the App is pretty much a requirement if you're a facebook user, even with the FB integration on the phone...))
Unless Facebook makes changes to remedy it, this issue is always going to exist, but they had to do it to ensure that communication is reliable on their social networks. A lot of people on FB use it primarily through a Web Browser, and with the Chat Module turned off (it can be intrusive, I've ALWAYS had it turned off and my PC is a beast). Agregating all message types into a single user interface makes for a better user experience on the web. In the future, who knows, they may do away with the actual IM service and just do PUSHed Messages, anyways...
Apps simply need to build in support for Pushing both FB Messages and FB IM and agregating it into one feed, then you won't have to worry about the breaks.
The issue I described with the chat client breaking happens also with Windows Live Messenger. It has nothing to do with Facebook. The IM client in Mango is just bad at handling multiple points of presence. I tested it across 4 platforms with over 6 IM clients. Only the WP7 client breaks in that way.