The main objective of this work is to propose a partial recoverable cohesive interface model, coupled with a bi-potential contact algorithm, to simulate the phenomenon of adhesion recoverability degradation under cyclic bonding–debonding between hyperelastic bodies. For this end, the proposed adhesion recoverability degradation model is constructed by defining the recovery of interface damage during the rebonding when two bodies come into contact, and a degradation factor related to the number of bonding–debonding cycles is introduced into the fully recoverable adhesion model to reduce energy dissipation after multiple cycles. Recoverability degradation includes adhesive stiffness and strength degradation, which is physically described as parallel, series and mixed arrays of adhesive bonds. Then, a finite element framework coupling the adhesion recoverability degradation model and the bi-potential contact algorithm is proposed, with Mooney–Rivlin hyperelastic material used to describe the soft matters. This framework is implemented in an in-house finite element code, with numerical examples demonstrating the model's reliability. The proposed approach could be applied to investigate interfacial adhesion effects in fields such as flexible electronics and intelligent robotics.