I did not say that it is impossible to set a timeout less than 120 seconds. You are missing 120 seconds for some operations before the dialog is displayed. That is, on the contrary, you need to set more time (increase the timeout).
Unfortunately, I do not know anything about ChronoSync, so I can hardly help further.
There is a way this script can timeout. It has to do with the Display Dialog command.
It depends on how the script gets called (I.E. from which program).
If that program is not the frontmost then the dialog doesn’t appear until it is brought to the front.
If the user never brings the program to the front it will timeout.
Is the script a standalone app or a compiled script?
Activate me will work with a standalone app, but you might have to be more specific by naming the app that is running the script.
Also you should use the “Display Alert” command if there is only one button, much simpler.
tell application "loginwindow" to display alert "Email backup is now finished;
feel free to mail again!" giving up after 6