As I wrote, you just have to add logic that will initialize the shift register only the first time...See the attached example.
In the attached example I make use of the fact that a boolean shift register will the very first time it is loaded have the value False...so if it's false I initialize the time stamp and set it to true...If you want to start over again you will need to unload the VI from meory to get the shift register back to false...However, you can just as easily let a button control the initialization instead...set the button to true when you want a new time stamp.