Effective seizure detection from long-term EEG is highly important for seizure diagnosis. Existing methods usually design the feature and classifier individually, while little work has been done for the simultaneous optimization of the two parts. This work proposes a deep network to jointly learn a feature and a classifier so that they could help each other to make the whole system optimal. To deal with the challenge of the impulsive noises and outliers caused by EMG artifacts in EEG signals, we formulate a robust stacked autoencoder (R-SAE) as a part of the network to learn an effective feature. In R-SAE, the maximum correntropy criterion (MCC) is proposed to reduce the effect of noise/outliers. Unlike the mean square error (MSE), the output of the new kernel MCC increases more slowly than that of MSE when the input goes away from the center. Thus, the effect of those noises/outliers positioned far away from the center can be suppressed. The proposed method is evaluated on six patients of 33.6 hours of scalp EEG data. Our method achieves a sensitivity of 100% and a specificity of 99%, which is promising for clinical applications.