The rapid development of Internet of Things (IoT) technology has led to increased attention to its potential applications in agriculture. IoT-based agricultural applications are able to better monitor crops and make informed decisions about resource allocation. Ensuring data reliability is a significant challenge in agricultural IoT environments. The reliability of collected data is subject to situational characteristics of IoT devices, such as their location, which can be easily compromised by environmental and human factors. To address this issue, location-based device authentication has been proposed as a means of ensuring data reliability. Currently, Physical Unclonable Function (PUF) is also widely used in IoT authentication mechanisms. In this paper, we propose a lightweight two-factor continuous authentication protocol based on PUF and location. The proposed protocol leverages the properties of PUF to resist physical attacks, uses simple cryptographic operations such as XORs and hash functions to ensure security, and reduces resource consumption through continuous authentication. A formal security analysis of the proposed scheme is performed using Burrows-Abadi-Needham (BAN) logic analysis. The informal security analysis of the proposed scheme demonstrates that it is resistant to several known attacks. Additionally, we further evaluate the performance of the proposed scheme. The results demonstrate that the proposed scheme has low communication and computational costs, and offers better security and functionality attributes.