If there is no exact date, what was the context of its downfall?
If you include ceremonial use, armour never disappeared from military use.
On the European battlefield, armour became scarce in the late 17th century. It didn't disappear completely - some cavalry units continued to wear steel breastplates and helmets, with some units still wearing breastplates in action in the early stages of World War I. When they stopped wearing them in action (early in WW1), you could say that this was an end of armour being used in the military, if
you ignore ceremonial military use,
you don't consider the leather Pickelhaube helmet to be armour, and
you don't count armoured fighting vehicles as armour (the first armoured cars predate WW1 by about 10 years).
But, if you count it as an end of armour, it was a very brief end, since the French issued steel helmets in 1915 (followed by other combatants), and steel body armour was being issued in WW1 by various combatants from 1916 onwards, and body armour and helmets have been in military use since then, with body armour becoming more common in late WW2 and afterwards.
Armour becoming scarce on the battlefield in the late 17th century was due to improved performance of guns leading to armour needing to be very thick to stop bullets. Very thick means very heavy, and armour was either discarded completely, or reduced to cuirass (sometimes just the breastplate) and helmet.