Keep time. Never leave all avenues open. Marrying players to a time table provides a sense of reality that helps underlie your game and help them suspend their belief. With a time table, you can inject holidays, festivals, seasons, and other events in a sensible and believable way.
This can lead to a mile of adventures, plot hooks and machinations that players can latch on. It really hits home the disparity between the long-lived/immortals and the rest of the worlds.
If you are interested in running "legacy" games, where the child of one character is played and so on, you'll need a time table to show