Your calendar is designed to display upcoming events only on your booking page. For many users, old events can clutter the database. Currently there is no function to delete old events in the calendar, but you can do the following:
You have to manually delete the old events from your database table. Here is the MySQL command (you can use a database management program such as PhpMyAdmin):
DELETE * FROM wp_posts WHERE wp_posts.id IN (SELECT wp_ai1ec_events.post_id FROM wp_ai1ec_events WHERE start < 1503597968)
where 1503597968 is the current unix epoch timestamp (used by MySQL).
Then also:
DELETE * FROM wp_ai1ec_events WHERE end < 1503597968;
DELETE * FROM wp_ai1ec_event_instances WHERE end < 1503597968;
To get the current unix epoch timestamp at any other time, use:
https://www.epochconverter.com/