MSE vs Cross Entropy for training with facial landmark (pose) heatmaps
I experienced a similar problem while doing pose estimation. Your problem may be due to the huge amount of "background" pixels, where the gaussian heatmap has very small values. So the network simply learns the trivial solution and sets the whole heatmap to zero, which results in a small mse error.

Solution to my problem was:

1) weigh the heatmaps: weigh pixels in the loss function, which are "foreground" more. For example you could count the percentage of "foreground" pixels and the percentage of "background" pixels for each heatmap and weigh foreground pixels with (1-percentage of foreground pixels) and background pixels with (1-percentage of background pixels)

2) Increase the maximum of the gaussians to ~12