For those not used to altering URLs I have posted examples showing exactly what bhrubin correctly states needs changing.

Below is the wrong code as shown by TripIt

https://www.tripit.com/feed/ical/private/<this will be your code specific>/tripit.ics

Below is the correctly amended version without the www.

https://tripit.com/feed/ical/private/<this will be your code specific>/tripit.ics

I hope this helps.