Organic electrochemical transistors (OECTs) have attracted considerable interest in the context of wearable and implantable biosensors due to their remarkable signal amplification combined with seamless integration into biological systems. These properties underlie OECTs' potential utility across a range of bioelectronic applications. One of the main challenges to their practical applications is the mechanical limitation of PEDOT:PSS, the most typical conductive polymer used as a channel layer, when the OECTs are applied to implantable and stretchable bioelectronics. In this work, we address this critical issue by employing natural rubber latex (NRL) as an additive in PEDOT:PSS to improve flexibility and stretchability of the OECT channels. Although the inclusion of NRL leads to a decrease in transconductance, mainly due to a reduced carrier mobility from 0.3 to 0.1 cm2/V·s, the OECTs maintain satisfactory transconductance, exceeding 5 mS. Furthermore, it is demonstrated that the OECTs exhibit excellent mechanical stability while maintaining their performance even after 100 repetitive bending cycles. This work, therefore, suggests that the NRL/PEDOT:PSS composite film can be deployed for wearable/implantable applications, where high mechanical stability is needed. This finding opens up new avenues for practical use of OECTs in more robust and versatile wearable and implantable biosensors.