The Ember Mug and Ember Mug² are both safe to keep on the charger when not in use. When the battery is fully charged, the charging is shut off automatically, so no battery damage will occur. We also have something called maintenance charging, which means that if left on the coaster for months on end, the battery is periodically topped off because the battery slowly self-discharges.
Please note - the Ember should be charged every couple of months even if it is not in use. Otherwise, the battery may become over discharged and could be damaged.