Fully automatic analysis of myocardial perfusion MRI datasets enables rapid and objective reporting of stress/rest studies in patients with suspected ischemic heart disease. Developing deep learning techniques that can analyze multi-center datasets despite limited training data and variations in software (pulse sequence) and hardware (scanner vendor) is an ongoing challenge. Datasets from 3 medical centers acquired at 3T (n = 150 subjects; 21,150 first-pass images) were included: an internal dataset (inD; n = 95) and two external datasets (exDs; n = 55) used for evaluating the robustness of the trained deep neural network (DNN) models against differences in pulse sequence (exD-1) and scanner vendor (exD-2). A subset of inD (n = 85) was used for training/validation of a pool of DNNs for segmentation, all using the same spatiotemporal U-Net architecture and hyperparameters but with different parameter initializations. We employed a space-time sliding-patch analysis approach that automatically yields a pixel-wise "uncertainty map" as a byproduct of the segmentation process. In our approach, dubbed Data Adaptive Uncertainty-Guided Space-time (DAUGS) analysis, a given test case is segmented by all members of the DNN pool and the resulting uncertainty maps are leveraged to automatically select the "best" one among the pool of solutions. For comparison, we also trained a DNN using the established approach with the same settings (hyperparameters, data augmentation, etc.). The proposed DAUGS analysis approach performed similarly to the established approach on the internal dataset (Dice score for the testing subset of inD: 0.896 ± 0.050 vs. 0.890 ± 0.049; p = n.s.) whereas it significantly outperformed on the external datasets (Dice for exD-1: 0.885 ± 0.040 vs. 0.849 ± 0.065, p < 0.005; Dice for exD-2: 0.811 ± 0.070 vs. 0.728 ± 0.149, p < 0.005). Moreover, the number of image series with "failed" segmentation (defined as having myocardial contours that include bloodpool or are noncontiguous in ≥1 segment) was significantly lower for the proposed vs. the established approach (4.3% vs. 17.1%, p < 0.0005). The proposed DAUGS analysis approach has the potential to improve the robustness of deep learning methods for segmentation of multi-center stress perfusion datasets with variations in the choice of pulse sequence, site location or scanner vendor.