The design of composite tissue scaffolds containing an extracellular matrix (ECM) and synthetic polymer fibers is a new approach to create bioactive scaffolds that can enhance cell function. Currently, studies investigating the effects of ECM-deposition and decellularization on polymer degradation are still lacking, as are data on optimizing the stability of the ECM-containing composite scaffolds during prolonged cell culture. In this study, we develop fibrous scaffolds using three polymer compositions, representing slow (E0000), medium (E0500), and fast (E1000) degrading materials, to investigate the stability, degradation, and mechanics of the scaffolds during ECM deposition and decellularization, and during the complete cellularization-decell-recell cycle. We report data on percent molecular weight (% Mw) retention of polymeric fiber mats, changes in scaffold stiffness, ECM deposition, and the presence of fibronectin after decellularization. We concluded that the fast degrading E1000 (Mw retention ≤ 50% after 28 days) was not sufficiently stable to allow scaffold handling after 28 days in culture, while the slow degradation of E0000 (Mw retention ≥ 80% in 28 days) did not allow deposited ECM to replace the polymer support. The scaffolds made from medium degrading E0500 (Mw retention about 60% at 28 days) allowed the gradual replacement of the polymer network with cell-derived ECM while maintaining the polymer network support. Thus, polymers with an intermediate rate of degradation, maintaining good scaffold handling properties after 28 days in culture, seem best suited for creating ECM-polymer composite scaffolds.