Electrochemical hydrogen evolution reaction (HER) at single graphene sheets has been investigated widely either in its pristine form or after chemical modification. One important challenge is the long-term stability of single graphene sheets on Si/SiO2 substrates under HER. Previous reports have found that due to stress developing under gas evolution, the sheets tend to break apart, with a very low lifetime limited to just a few cycles of HER. Here, we show through appropriate electrode preparation that it is possible to achieve highly durable single graphene electrodes on insulating substrates, which can survive several hundreds of HER cycles with virtually no damage to the sp2-carbon framework. Through systematic investigations including atomic force microscopy, Raman spectroscopy and electroanalysis, we show that even after so many cycles, the sheet is physically intact and the electron transfer capability of the electrodes remain unaffected. This extremely high stability of a single atomic sheet of carbon, when combined with appropriate chemical modification strategies, will pave way for the realization of novel 2D electrocatalysts.