Players can check for 4 types of content through Procyon’s Compass (the widget that displays active content), or by accessing the Calendar in the top-left of the HUD for the full schedule. Activity times are based on the local time of the server’s region.
If you drop out or leave the area while participating in these activities, the reward counter will not increment and you will have another chance to earn a reward.
Those are official notes too. I don’t know if failing a run with a pug on a event, then locking you out for more attempts is proper. Nor is there any other content that I’m aware of which follows the same logic.