In previous research, scholars always think about how to improve the information hiding algorithm and strive to have the largest embedding capacity and better image quality, restoring the original image. This research mainly proposes a new robust and reversible information hiding method, recurrent robust reversible data hiding (triple-RDH), with a recurrent round-trip embedding strategy. We embed the secret message in a quotient image to increase the image robustness. The pixel value is split into two parts, HiSB and LoSB. A recurrent round-trip embedding strategy (referred to as double R-TES) is designed to adjust the predictor and the recursive parameter values, so the pixel value carrying the secret data bits can be first shifted to the right and then shifted to the left, resulting in pixel invariance, so the embedding capacity can be effectively increased repeatedly. Experimental results show that the proposed triple-RDH method can effectively increase the embedding capacity up to 310,732 bits and maintain a certain level of image quality. Compared with the existing pixel error expansion (PEE) methods, the triple-RDH method not only has a high capacity but also has robustness for image processing against unintentional attacks. It can also be used for capacity and image quality according to the needs of the application, performing adjustable embedding.