Hello Mo,
This piece is entirely dependent on the settings you have in Task Scheduler and how you use your machine.
Firstly, I'm assuming the user's machine is still on and connected to the network when they're offline? If they're using a laptop, etc, maybe consider installing on a server or VM instead.
Secondly, if their machine isn't losing connection at any point, make sure the settings are correct for Task Scheduler. If you go to Start -> Windows Administrative Tools -> Task Scheduler and double click on the schedule, the first tab (General) has a setting to "Run whether user is logged on or not". You will need to provide credentials.
One last thing that comes to mind is to make sure that the Reports application is set to always run as administrator (you can right click on the executable and set this in properties and clicking on advanced) if you haven't done that.