The application of machine learning-based tele-rehabilitation faces the challenge of limited availability of data. To overcome this challenge, data augmentation techniques are commonly employed to generate synthetic data that reflect the configurations of real data. One such promising data augmentation technique is the Generative Adversarial Network (GAN). However, GANs have been found to suffer from mode collapse, a common issue where the generated data fails to capture all the relevant information from the original dataset. In this paper, we aim to address the problem of mode collapse in GAN-based data augmentation techniques for post-stroke assessment. We applied the GAN to generate synthetic data for two post-stroke rehabilitation datasets and observed that the original GAN suffered from mode collapse, as expected. To address this issue, we propose a Time Series Siamese GAN (TS-SGAN) that incorporates a Siamese network and an additional discriminator. Our analysis, using the longest common sub-sequence (LCSS), demonstrates that TS-SGAN generates data uniformly for all elements of two testing datasets, in contrast to the original GAN. To further evaluate the effectiveness of TS-SGAN, we encode the generated dataset into images using Gramian Angular Field and classify them using ResNet-18. Our results show that TS-SGAN achieves a significant accuracy increase of classification accuracy (35.2%-42.07%) for both selected datasets. This represents a substantial improvement over the original GAN.