I have recently had a lot of issues with Cisco ASDM on new installs of Windows 7 and upwards.
After lots of research and a bit of digging I have found a way to resolve this issue.
Install Java Runtime Environment 6 Update 7
Install ASDM onto the computer
Edit the properties it the ASDM Shortcut.
change the beginning of the target from:
C:\Program Files (x86)\Java\jre1.6.0_07\bin\javaw.exe
This should resolve the issue with version 7.1(1) not connecting to devices.