I have a small (bought) board here that flashes leds. I opened it up and found that each led + is driven by a S8550 PNP transistor (rated at Ic 0.5A).
I expect the leds attached were drawing in excess of the 0.5A at one point.

My problem is that the led isn't turning off completely - I can see it pulsing but it stays on all the time, never goes off completely.

Is this an indication that the transistor is failing?

 

Given your circuit description I am inclined to ask for an image of this circuit or at least a clear photograph of the board, front and back. Not sure what type of LED's they are, but most General purpose LED would be a little black ball of plastic if 500mA were to pass through them.

 

Originally the board was driving banks of leds (might have been around 22 leds each circuit), I've been trying it on a 10w LED.

As for the 500mA, I know I've pulsed 20mA leds with much higher currents for very short periods without damage. This board pulses are quite short duration too.

What I really need to know is how likely it is that if the transistor is failing it would be passing some current all the time.

Here are the images:

 

Damaged transistors do sometimes have increased leakage currents. Note that unless you know that the board was designed for as much as 500mA, the transistor maximum rating may not be the whole story. Those are small devices, and would need to be appropriately driven - preferably well saturated - to run at maximum collector current without overheating.

Unless the "10W" device used more than one junction in series junction, its maximum rated current could have been about 3A: How were you powering it?

 

I was using this board to drive the base of a TIP41A through a1k resistor with the 10w led connected to the TIP41A collector.

The problem arose when I tried powering the led + from this board too.