1. Literally, of a gas or liquid, to flow out and escape from (something) gradually but steadily, as through a leak, crack, puncture, etc. There must have be a leak in the oil tank of the car, because it keeps seeping away onto the driveway. Make sure you close the valve tight on that jar—we don't want any of the gas to seep away.

2. By extension, to dwindle or disappear gradually but steadily. The goodwill he had earned with his employers began seeping away after he started showing up to work late. Once the undisputed kings of Hollywood, the movie studios good fortunes began to seep away after a series of poor business decisions.