Without the penny soldered to the cathode, the LED should last anywhere between 3 seconds and 3-4 minutes with any current much over 120-150mA. Nichia LEDs tested to destruction have failed in this time frame with similar current levels. The penny soldered to the cathode is the only reason your LED hasn't yet popped.
It won't last much above what you're driving it, penny or not, because you'll start having problems with wirebond breakage, wirebond heating, melting or charring of the epoxy encapsulant in the vicinity of the wirebonds, and chemical changes to the LED die & phosphor.
If the bond wires and/or die get hot enough, carbon atoms present in the encapsulant material will dissociate to free carbon, and could eventually cause a short circuit between the anode and cathode just above the surface of the die.
I don't know how hot the phosphor can get before it goes bad; Nichia has not published that info. But like any complex molecule, there is a definite upper limit on its temperature before dissociation or other chemical changes begin to take place.
Cratering of the ball bonds also begins to occur at these seriously high temperatures, if the bond wires themselves don't melt off or carbonize the surrounding epoxy first. In either case, the LED will become intermittent or simply go out and the current in the circuit will drop to 0 or nearly 0. The wirebond may physically seperate from the surface of the die, usually taking a chunk of die with it. In the case of top bonded sapphire-substrated lamps, only the P- or N- layer will come up with the bond wire (depending on which wire pulls up); as the sapphire itself is so hard it would not break or chip off with a near-zero-force seperation like that. But the effect is the same: the LED flickers or goes out entirely.
The encapsulant itself will probably begin to discolor & darken even before it reaches charring temperatures. It could also crack or fracture. If it does this, you'll hear it pop or see a crack going partway or all the way around the LED about 1/3 up from the base. The LED will usually fail at this point, as the wirebonds are pulled off the chip by the seperation of the LED halves. Only on rare occasions does the epoxy fracture above the tops of the bond wire loops, sparing them.
The LED chip itself can get pretty toasty, but once it gets above a certain temperature, atomic dissociation will begin to enter the picture; as the surface temperature begins to approach those encountered during parts of the MOCVD process originally used to make the thing. Gases released from outgassing epoxy, phosphor slurry, and possibly even the material bonding the sapphire substrate to the cathode anvil could then react or chemically bond with the hot gallium nitride and change its chemical & electrical properties. I think the wirebonds would come off before this point though.
Permanent shifting of the 460nm spectral peak out of the phosphor's optimum response wavelength and significantly reduced output at this peak would be two expected consequences of this. The LED would become dim, possibly unusably so.
Cracking or crazing of the substrate could be possible in extreme conditions; if this happens, the circuit is broken and the LED again becomes intermittent or goes out.