Federated Learning (FL) enables numerous participants to train deep learning models collaboratively without exposing their personal, potentially sensitive data, making it a promising solution for data privacy in collaborative training. The distributed nature of FL and unvetted data, however, makes it inherently vulnerable to backdoor attacks: In this scenario, an adversary injects backdoor functionality into the centralized model during training, which can be triggered to cause the desired misclassification for a specific adversary-chosen input. A range of prior work establishes successful backdoor injection in an FL system; however, these backdoors are not demonstrated to be long-lasting. The backdoor functionality does not remain in the system if the adversary is removed from the training process since the centralized model parameters continuously mutate during successive FL training rounds. Therefore, in this work, we propose PerDoor, a persistent-by-construction backdoor injection technique for FL, driven by adversarial perturbation and targeting parameters of the centralized model that deviate less in successive FL rounds and contribute the least to the main task accuracy. An exhaustive evaluation considering an image classification scenario portrays on average $10.5\times$ persistence over multiple FL rounds compared to traditional backdoor attacks. Through experiments, we further exhibit the potency of PerDoor in the presence of state-of-the-art backdoor prevention techniques in an FL system. Additionally, the operation of adversarial perturbation also assists PerDoor in developing non-uniform trigger patterns for backdoor inputs compared to uniform triggers (with fixed patterns and locations) of existing backdoor techniques, which are prone to be easily mitigated.