A real-time assessment of sustained attention requires a continuous performance measure ideally obtained objectively and without disrupting the ongoing behavioral patterns. In this work, we investigate whether the phasic functional connectivity patterns from short- and long-range attention networks can predict the tonic performance in a long Sustained Attention to Response Task (SART). Pre-trial phase synchrony indices (PSIs) from individual experiment blocks are used as features for assessment of the proposed average cumulative vigilance score (CVS) and hit response time (HRT). Deep neural networks (DNNs) with the mean-squared-error (MSE) loss function outperformed the ones with mean-absolute-error (MAE) in 4-fold cross-validations. PSI features from the 16-20 Hz beta sub-band obtained the lowest RMSE of 0.043 and highest correlation of 0.806 for predicting the average CVS, and the alpha oscillation PSIs resulted in an RMSE of 51.91 ms and a correlation of 0.903 for predicting the mean HRT. The proposed system can be used for monitoring performance of users susceptible to hypo- or hyper-vigilance and the subsequent system adaptation without implemented eye trackers. To the best of our knowledge, functional connectivity features in general and phase locking values in particular have not been used for regression models of vigilance variations with neural networks.