This seems like a pretty obvious question but the answer is not so obvious. The Rambam in the Sefer Hamitzvos explains that we need to kepp dinim d'rabbanan based on לא תסור. In other words there is a חיוב מן התורה to keep dinim d'rabbanan. The Ramban there disagrees and asks on the Rambam, if there is a חיוב מן התורה then why are we מחלק between dinim d'rabbanon and d'oraysas? If every din d'rabbanan is really a d'oraysa then why do we say ספקא דרבנן לקולא?
We see clearly from the Ramban that he holds that there is no חיוב מן התורה to kepp dinim d'rabbanan. If so what is the מחייב?
R' Elchanan in קונטרוס דברי סופרים has the following fascinating suggestion. He suggests that there really is no מחייב. He says that why do we keep d'oraysa's? Because we want to do the רצון hashem. The same applies to dinim d'rabbanan. we assume that whatever the חכמים were מתקן is the רצון hashem and therefore we keep them because we want to do the רצון hashem.