Active object systems are a model of distributed computation that has been adopted for modelling distributed systems and business process workflows. This field of modelling is, in essence, concurrent and resource-aware, motivating the development of resource-aware formalisations on the active object model. The contributions of this work are the development of a core calculus for resource-aware active objects together with a type system ensuring that well-typed programs are fairly terminating, i.e., they can always eventually terminate. To achieve this, we combine techniques from graded semantics and type systems, which are quite well understood for sequential programs, with those for fair termination, which have been developed for synchronous sessions.