Unsupervised monocular trained depth estimation models make use of adjacent frames as a supervisory signal during the training phase. However, temporally correlated frames are also available at inference time for many clinical applications, e.g., surgical navigation. The vast majority of monocular systems do not exploit this valuable signal that could be deployed to enhance the depth estimates. Those that do, achieve only limited gains due to the unique challenges in endoscopic scenes, such as low and homogeneous textures and inter-frame brightness fluctuations. In this work, we present SMUDLP, a novel and unsupervised paradigm for multi-frame monocular endoscopic depth estimation. The SMUDLP integrates a learnable patchmatch module to adaptively increase the discriminative ability in low-texture and homogeneous-texture regions, and enforces cross-teaching and self-teaching consistencies to provide efficacious regularizations towards brightness fluctuations. Our detailed experiments on both SCARED and Hamlyn datasets indicate that the SMUDLP exceeds state-of-the-art competitors by a large margin, including those that use single or multiple frames at inference time. The source code and trained models will be publicly available upon the acceptance.