We present an accurate, fast and efficient method for segmentation and muscle mask propagation in 3D freehand ultrasound data, towards accurate volume quantification. To this end, we propose a deep Siamese 3D Encoder-Decoder network that captures the evolution of the muscle appearance and shape for contiguous slices and uses it to propagate a reference mask annotated by a clinical expert. To handle longer changes of the muscle shape over the entire volume and to provide an accurate propagation, we devised a Bidirectional Long Short Term Memory module. To train our model with a minimal amount of training samples, we propose a strategy to combine learning from few annotated 2D ultrasound slices with sequential pseudo-labeling of the unannotated slices. To promote few-shot learning, we propose a decremental update of the objective function to guide the model convergence in the absence of large amounts of annotated data. Finally, to handle the class-imbalance between foreground and background muscle pixels, we propose a parametric Tversky loss function that learns to adaptively penalize false positives and false negatives. We validate our approach for the segmentation, label propagation, and volume computation of the three low-limb muscles on a dataset of 44 subjects. We achieve a dice score coefficient of over 95 % and a small fraction of error with 1.6035 ± 0.587.