if you knew the amount of current those LEDs were being driven with, you could calculate a suitable resistor value to put in in place of the one that burned out, for instance, 100mA would give 3.6V/0.1A=36 ohms, and the resistor would dissipate 3.6V*0.1A=.36W, so a half watt resistor would work there... that resistor might also act as somewhat of a fuse in case an LED in the string shorts rather than failing open circuit.
i just did a quick calculation of 5W/9LEDS=0.555W... .555W/3.6V=.154A so 150mA would make it 24 ohms, dissipating .555W, so a 1 watt resistor would be required