There are a bunch of ways to do what you want. Most involve shift registers or local or global variables.
If I understand you, you want to keep track of the cumulative time while the Save button is pressed. If Save is on and you get to (e.g.) 5 minutes, then Save is turned off for any amount of time. When Save is pressed again, you want to start at 5 minutes.
The easiest way to do this is to forget the iteration counter and use a shift register on your while loop. Right click on a vertical border of your while loop and select Add Shift Register. Create an integer constant of 0 outside of the while loop and wire it to the left shift register terminal. Inside your while loop, wire your left shift register terminal to the left side of your Save case, and w
ire the right shift register terminal to the right side of your Save case. In your Save True case, add 1 to the left shift register terminal then pass it to the right shift register terminal. In your Save False case, wire the left shift register terminal straight through to the right shift register terminal. Calculate your time as you did before.