The agent’s path is calculated the moment it is created. If the agent can make the relevant trip within the 20 minute time limit, it proceeds. I’m assuming the path is recalculated over the course of the journey and if it is found to exceed the limit, the agent is removed (due to “unforeseen” complications be it to user action or otherwise). Same thing happens if the point of origin (or destination) is removed. Again, the same applies if the POD and POO are redeveloped by the AI.
All this is based purely on my observation. It would behoove the developers to take their finger out and write a sticky on agent behaviour since that is the basis for the whole economy ffs.