Depends on the construction of the diode, the point where the diode fails from over current is when it's junction temperature reaches a certain level, at that point the materials in the junction will change, either decomposing or simply mixing destroying the normally structured diode material's characteristics.
It's always best to drive an LED at it's rated current, it will last longest that way, or even bellow it's rated current it may last longer than it's user.. Doubling the current through it will give you a higher output, but it won't be double. Diodes, like pretty much any real world device have an efficiency curve associated with them.
While with PWM the average package temperature is okay the instantaneous temperature of the junction during conduction is higher. Increased (even peak well within average condition acceptability) thermal conditions will cause increased junction degradation, and eventual device failure.
I mean if you connect an IR diode to the terminals of a 12 volt battery it will produce a very bright IR pulse, at least some of which will come from the package bursting into flames... That's one extreme, but every ma you exceed the diode's rated current for will get you that much closer to the failure point sooner. Basically every moment at a given temperature ages a diode a certain amount, the higher the temperature the higher the aging effect. At bellow nominal levels, you have to worry about the package wearing out before you have to worry about a junction temperature issues.