Howdy Jaimendt, and welcome to CPF, sorry to hear you're having an issue with your SC600w.
My first instinct is that it's the battery, as that's what will typically happen with a close to fully discharged battery. Do you have any other batteries that you can use to check the light? How do you know that battery is fully charged? Have you checked it with a meter, or are you relying on your battery charger's indicator light? What kind of battery is it (brand, mAh rating, and is it protected or unprotected) and how old is it? What kind of charger are you using?
How long have you owned the light and has it always worked well up to now, or did you just purchase it (new or 2nd hand)? Have you tried turning the light on in the low mode to see if it will keep running at that level?
Of course, it's also typical in these situations to go ahead and clean all the contact points in the light, just for good measure, with the main ones being 1.) the positive terminal in the head, 2.) the negative contact point, which is the tip of the spring in the tailcap, 3.) the area in the tailcap inside at the bottom that goes around the outer edge (which makes contact with the body tube when they are screwed together), and 4.) the edge of the body tube (which makes contact with the inside of the tailcap).
Electrical contact cleaner is best, but you can always use isopropyl alcohol, the kind you typically find in your medicine chest, and a Q-tip, or even a clean pencil eraser. When cleaning the positive contact point in the head, be sure and hold the head face up, with the battery opening facing down, so as to not have any of the wet cleaner drip down into any electrical areas, and always apply the cleaner to the Q-tip, not the flashlight.
Anyway, give us some more information and we will try to help you find the problem.
EDIT: Oh, and while your cleaning things, be sure and clean both ends of the battery, and while I doubt it has anything to do with it, with the charger unplugged, you could clean the battery contact points on the charger as well.