Offline messaging broken
Offline messages in Messenger have always been stored on Hotmail (now Outlook.com), and with the e-mail count and notifications for Outlook.com in Messenger being removed recently, it was no surprise when the reports that offline messaging was no longer working. I can sadly confirm that to be the case.
However, it’s more complicated than simply being gone. Your offline messages can be triggered to be sent to you in Messenger… by using Skype.
If you want to try this yourself, link your Messenger Microsoft account to a Skype ID. Then with Messenger signed in already, log into Skype using your normal Skype username (you could use your Microsoft account as well, but you don’t have to). As soon as Skype logs in, your offline message will magically appear in Messenger. Note this requires Messenger 2012, it does not seem to work on 2009.
Additionally, you can also see your offline messages by using Outlook.com’s web messaging feature by signing in with your Microsoft account (note that it does not need to be a Live/Hotmail address to work).