Jumping off chain can be from a worn out chain - hold it out sideways with the link pins vertical, if it droops down in an arch instead of sticking straight out it is well worn, stretched out.... This will make the links longer than the sprocket teeth spaces and it works itself off. Also wears out the sprocket.
Or, the sprockets don't line up, worn bearing, bushing, etc could make one sprocket not be parallel to the other, or shaft moved or sprocket slipped sideways so they aren't in line.
Or, if an idler is worn that it tracks sideways, pulling the chain out of line with the 2 sprockets. Often it works longer than you would think if the other 2 points are not a problem, but at some point it will be bad enough to cause a problem.