In this paper, we investigate the periodic peeling behavior of opposing symmetric peeling fronts involving an elastic tape peeled off from a deformable substrate of finite thickness, backed onto a rigid foundation.We treat the problem by means of an energetic formulation, and we found that, depending on the values of the initial detached length l, substrate thickness h, and peeling periodicity λ, the translational invariance of the peeling process is lost and restored, as the elastic interaction between the peeling fronts is limited by the substrate thickness. Indeed, given h and λ, a critical value of the detached length can be found, which is able to prevent unstable peeling of the tape under a fixed applied load, thus resulting in enhanced adhesion strength, with respect to the classical Kendall's solution for peeling from a rigid substrate. On the other hand, given the geometrical system configuration (i.e. the detached length l) the load necessary to trigger the peeling can be minimized by conveniently tuning the ratio h/λ. This feature might be of interest for the development of innovative designs for future biomedical devices, such as Transdermal Drug Delivery Systems or wound dressing, requiring low peel adhesion for safe successive removals.