Physical Unclonable Functions (PUFs) are popular hardware security primitives that offer lightweight authentication for constrained devices. However, lightweight PUF-based authentication often limits the number of authentications provided or even throttle the device to prevent adversaries from collecting enough information that could compromise the device\'s security. This work introduces a Shadow PUF design, a controlled Strong PUF, to secure challenge-response exchanges from attackers and allow for an unlimited generation of unique responses. The proposed Shadow PUF design ensures security by periodically reconfiguring its behavior. The reconfiguration bits are generated by a static PUF primitive and never exposed; While, all authentication exchanges are done using the reconfigurable Shadow PUF. An ASIC Synthesis of the Shadow PUF demonstrates its small implementation area requirements and low power consumption. The security of the proposed PUF design against modeling attacks has also been analyzed.