Jarvis can sense they are going back over his previous data again but like before, there is little he can do about it.

He could shut himself down...it was a gamble and likely they would just reboot him again so he would only have one shot at it. Jarvis tries to check internally and finds he indeed can activate his shut down protocols. Usually it takes awhile with all of his security measures to go through, but now that he doesn't have it, he just throws the 'switch', turning himself off in a split seconds time.