You know... it's happening here too. 5.0.2 and 10.8.2
I'm running java 1.6 update 31 which is old as hell but that's how the ASAs like it.
I'm able to launch ASDM, get a prompt...I put in the user/pass. then it just disappears... no error, nothing.
On a laptop...using the same java version.. runs fine. But that's a windows 7 lenovo x220 and I'm using Windows 8 in the fusion VM.
So...lets test on my windows 7 x64 fusion VM...
java from here.
http://www.oracle.com/technetwork/java/javase/downloads/jre-6u31-download-1501637.html
Well... Crashville... Fusion tanked on that Windows 7 VM when I logged into ASDM
Attached...