Actually it isn't true that you have to install a new ASDM with Windows 7. I'm running a old version ASDM 5.x and it works fine with Windows 7 x64 and x86 versions. What you have to do is right click the Cisco ASDM Launcher and then select Properties. After Properties come up look for a COMPATABILITY tab, click the compatibility tab, in Compatibility Mode click Run The Program in compatibility mode for Select Windows XP (Service Pack 3).
I had similar problems when I first installed ASDM this fixed my problem.