You can access your TripIt account without wifi/connectivity.
You will be able to access your travel information when you do not have connectivity as long as you leave your app signed in (i.e. don't sign out when last viewing your account). The one caveat is that information will be static; no updates will display until you next have connectivity.
As an added precaution we recommend taking screen shots of your itinerary.
Updated: Aug 26, 2016