Efficient compression of electroencephalogram (EEG) signals is crucial for enabling real-time monitoring, storage, and transmission in various medical and non-medical applications. This paper presents a segment-wise processing approach using temporal modeling-based auto encoders for EEG signal compression. By leveraging models such as Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Recurrent Neural Network (RNN), and Self-Attention, the proposed method effectively captures temporal dependencies in the EEG data. Segment-wise processing not only enhances compression efficiency but also significantly reduces the processing time of these sequence models. Extensive experiments demonstrate that GRU-based auto encoders offer the best performance, particularly at lower Data Reduction Factors (DRFs), achieving a minimal signal loss of 0.2% at a 50% compression ratio, making it suitable for medical applications. For non-medical scenarios, a higher compression ratio of 75% with a signal loss of 5.4% is found to be acceptable. The results indicate that the proposed approach achieves a favorable balance between compression efficiency, signal fidelity, and computational performance.