Monocular visual simultaneous localization and mapping (V-SLAM) is nowadays an irreplaceable tool in mobile robotics and augmented reality, where it performs robustly. However, human colonoscopies pose formidable challenges like occlusions, blur, light changes, lack of texture, deformation, water jets or tool interaction, which result in very frequent tracking losses. ORB-SLAM3, the top performing multiple-map V-SLAM, is unable to recover from them by merging sub-maps or relocalizing the camera, due to the poor performance of its place recognition algorithm based on ORB features and DBoW2 bag-of-words. We present CudaSIFT-SLAM, the first V-SLAM system able to process complete human colonoscopies in real-time. To overcome the limitations of ORB-SLAM3, we use SIFT instead of ORB features and replace the DBoW2 direct index with the more computationally demanding brute-force matching, being able to successfully match images separated in time for relocation and map merging. Real-time performance is achieved thanks to CudaSIFT, a GPU implementation for SIFT extraction and brute-force matching. We benchmark our system in the C3VD phantom colon dataset, and in a full real colonoscopy from the Endomapper dataset, demonstrating the capabilities to merge sub-maps and relocate in them, obtaining significantly longer sub-maps. Our system successfully maps in real-time 88 % of the frames in the C3VD dataset. In a real screening colonoscopy, despite the much higher prevalence of occluded and blurred frames, the mapping coverage is 53 % in carefully explored areas and 38 % in the full sequence, a 70 % improvement over ORB-SLAM3.