Like many others (judging from Google), I have been having problems with Windows Live Messenger stability under Windows 7 (I'm using the 64-bit Enterprise version). The stability problems manifest as inability to log in, or, if you can log in, as bounced messages or random and frequent dropping out of connectivity.
The puzzling thing is that there is no problem with WLM if I first connect to my work VPN, and other PCs on my home network running XP also have no problems.
My security software is Microsoft Security Essentials, and what seems to have resolved the issue is to add WLM and associated services to MSE as "Excluded Processes" under the Settings tab. I added all 4 executables in the Messenger program group (i.e. msnmsgr.exe, msvs.exe, wlcsdk.exe, wlcstart.exe), and Messenger has been stable ever since. I hope this helps someone else wrestling with WLM!