There could be a few reasons why the button stopped working, particularly for older chargers - or chargers that have been unused for a longer period. The contact surfaces of the MODE button may have oxidized and become stuck.
Please try the following:
Connect the charger to the mains.
Power on the charger but leave disconnected from a battery, periodically pressing the MODE button as this may help remove any oxidation.
Also try pressing the mode button a litle firmer and repeat several times.
If the issue persists, the button is most likely defective. However, please keep in mind that the charger will still work in the selected mode.