I would advise someone to not leave it any closer than two hours before a flight but i have changed peoples flights when it was a lot closer right upto 45 min before a flight.technically for a international flight out of heathrow a flight should be changed before this point as otherwise its technically a noshow as you would need ti be through security before this point.

A reissue itself doesnt take that long once payment details are given and flight is agreed its getting the calculation for a change which does take time. Its really making sure you leave enough time to call up as a call may be needed!