Although deep learning has received much attention for accelerated MRI reconstruction, it shows instabilities to certain tiny perturbations resulting in substantial artifacts. There has been limited work comparing the stability of DL reconstruction with conventional reconstruction methods such as parallel imaging and compressed sensing. In this work, we investigate the instabilities of conventional methods and the Variational Network (VN) with different accelerations. Our results suggest that CG-SENSE with an optional regularization is also impacted by perturbations but shows less artifacts than the VN. Each reconstruction method becomes more vulnerable with higher acceleration and VN shows severe artifacts with 8-fold acceleration.