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.
1. Install Java Runtime Environment 6 Update 7
2. Install ASDM onto the computer
3. Edit the properties it the ASDM Shortcut.
4. 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.