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The charge density wave (CDW) state in van der Waals systems shows interesting scaling phenomena as the number of layers can significantly affect the CDW transition temperature, $T_{CDW}$. However, it is often difficult to use conventional methods to study the phase transition in these systems due to their small size and sensitivity to degradation. Degradation is an important parameter which has been shown to greatly influence the superconductivity in layered systems. Since the CDW state competes with the onset of superconductivity, it is expected that $T_{CDW}$ will also be affected by the degradation. Here, we probe the CDW phase transition by the mechanical resonances of suspended 2H-TaS2 and 2H-TaSe2 membranes and study the effect of disorder on the CDW state. Pristine flakes show the transition near the reported values of 75 K and 122 K respectively. We then study the effect of degradation on 2H-TaS2 which displays an enhancement of $T_{CDW}$ up to 129 K after degradation in ambient air. Finally, we study a sample with local degradation and observe that multiple phase transitions occur at 87 K, 103 K and 118 K with a hysteresis in temperature in the same membrane. The observed spatial variations in the Raman spectra suggest that variations in crystal structure cause domains with different transition temperatures which could result in the hysteresis. This work shows the potential of using nanomechanical resonance to characterize the CDW in suspended 2D materials and demonstrate that degradation can have a large effect on transition temperatures., The following article has been accepted by Applied Physics Letters. After it is published, it will be found at [https://doi.org/10.1063/5.0051112]