Polymer degradation and mechanical properties are of paramount importance in tissue engineering. The degradation rate of polymeric scaffolds is influenced by several important material and environmental factors. In particular, the mechanical support provided by the scaffold to the surrounding tissue during tissue regeneration is critical for that it directly impacts the cell behavior through mechanical signals sensed by mechanoreceptors on the cell surface. Consequently, the principal objective of the present study was to investigate the degradation behavior of electrospun poly-L-lactic acid (PLLA) bilayer microfibrous scaffolds in pH-neutral medium. Changes in the morphology, molecular weight, crystallinity, mass loss, and thermomechanical properties of the scaffolds over an extended period were studied by scanning electron microscopy, differential scanning calorimetry, gel permeation chromatography, and tensile testing. An interplay between chain scission and orderly chain rearrangement in the polymer scaffold commenced during degradation, leading to the decrease of the molecular weight and stiffness, a constant mass loss, and an increase in crystallinity, tensile strength, and glass transition temperature, with virtually constant yield strength and melting temperature. The unchanged structure morphology and adequate matrix stiffness after prolonged degradation illuminated the potential of the bilayer PLLA scaffolds for tissue engineering and drug delivery applications. Nonetheless, modifications to the scaffold structure or surface may be required to accordingly tune the degradation rate in these applications. The experimental methodology introduced in this study can be extended to potentially investigate material degradation in other fields, such as agriculture, packaging, and disposable products.