Windex works very well to remove this kind of thing, but straight ammonia diluted with water works just as well.
I have used Windex several times on a area on the north side the needs it every few years. Just spray the Windex on and scrub it with a scrub brush. As suggested, the long handle version helps to avoid moving the ladder as often. Rinse by spraying down with a hose sprayer on full. You can use the jet setting as well but be careful to avoid spraying up as the water will get under the siding if you're not careful. Wet down the area with the hose and then, as suggested, apply the Windex and scrub from the bottom up and then rinse with the hose from the top down. Don't let the Windex dry on the siding or you will start over again. With ammonia, you can just have a bucket of ammonia and water and keep dipping the scrub brush in. You can also put the ammonia and water in a spray bottle if you have one. A big pump sprayer works well for this so your hand doesn't get tired squeezing the trigger.
If stains are stubborn, just apply more Windex and let it sit for a while.
As I said, straight ammonia diluted with water will work just as well as Windex and cost allot less. I had a huge jug of Windex so I just used that but I have used ammonia as well. I have cleaned vinyl fencing with the same problem using ammonia and water.
Windex or ammonia does not prevent this from coming back every few years but it is very cheap. If you try a product that is intended to be preventative, I would be interested to hear how that turns out.
I used a mixture of bleach and TSP when the same area was wood shingle and had the same problem. The wood involved allot more scrubbing and some penetration into the wood to kill what was growing. I have never bothered with bleach on the vinyl since Windex or ammonia works so well and you don't have to be careful with clothing and such. Possibly the bleach prevents it from coming back so quickly.
With the Windex or ammonia I have to do the job every three years or so. I wouldn't bother with anything expensive if it doesn't work for longer than that. You probably have a jug of ammonia around already so you could try it and see what you think.
LMHmedchem