Can a door be shut while in flight?
I've had this happen a few times on aging C152's and in all cases I have been able to simply push it against the airflow enough to pull it closed. On a PA28 with the door the other side of the cabin from the pilot seat, this wouldnt be possible. Not that I have experienced it in a PA28, but I might ask a passenger to attempt the same (hard push followed by a hard pull).

Some things to note:


There's no massive danger of a door slightly ajar, so waiting until  out of a critical phase of flight is advisable (ie, climbed to cruise, clear of any ATZ)
In all but one time I had another competent pilot sitting next to me who can keep an eye out and even hold the controls for a few seconds. Just one reason flying with other pilots is nicer than flying alone.


However, I would suggest that every situation is different. The most important thing is, as always, Aviate first. A light aircraft is unlikely to be critically unable to continue flying with a door ajar. Don't get distracted by something like an ajar door - fly the aircraft.

If in any doubt, land as soon as possible and fix the problem. It would, I think, be acceptable to call "Pan Pan" if you feel you need to expedite a landing.