Armor and Weapons have a durability statistic displayed at the bottom of the item gump when you mouse-over the item, it looks like 150/200. If the max durability number drops to zero there is a chance the item will break and disappear.
An items durability is comprised of two parts: the current durability, and the maximum durability, both of which are values in the range of 0-255.
The Current Durability on an item is decreased through hitting monsters, animals, or other players, as in the case of weapons, or through being hit by monsters, animals, or other players, as in the case of armor and shields.
The self repair property automatically repairs some of the damage that the item has taken.
When an item takes damage, the Self Repair property adds durability equal to its intensity (so SR 1 would add one point, SR 5 would add 5 points.)
It then sets a timer, and Self Repair doesn't go off again on that item for 60 seconds, even if the item gets damaged again.
Your item may take also substantial damage quickly by an acid attack and may not repair fast enough to compensate for the damage.