Have used TI 2011 W/Plus Pack extensively on 2-5 different PCs and never had this problem.
I even used it to move Win 7 Pro Retail upgrade from my older Core 2 Duo system to my new i5 760 system using the universal restore feature of Plus Pack. Worked first time, never had any problem with activation.
By chance do you have this same copy of 7, using the same key, installed on a different PCs on your network?
The reason I ask is when setting up my new system I also moved the XP install I had on my old system to the new system figuring I'd change the registration key after I got it setup, I have 3 licenses for XP. What I didn't do was turn off the other system that was running XP using that same key. When XP on my new system loaded it looked at the other system on my LAN and found the other that had the same key. It then came up with a error, "This product is illegal" never giving me the chance to change the key. So I had to reinstall using one of my other licenses.
Could also be you have changed enough hardware to trigger a RE-Activation. It will happen sooner with a OEM version/key then with a retail version/key because the OEM version is non transferable so it looks for changes in hardware more closely.
So are you using a Retail or OEM version/key.