I had issues similar to OP's with my 10 y.o. and it is an ongoing thing to keep him on track and semi-organized, but his teachers are fully on board with this and email me regularly when he seems to be veering off-course. I'm grateful to them because I get the "nope, no homework tonight" thing on a regular basis -- luckily I know better!
A couple of things come to mind -- has he been tested for learning disabilities, for ADD/ADHD? What is his end of day routine? We had issues with bringing stuff home because DS had to run to catch the bus after school and the driver waited for NO ONE! Once we got that figured out things were a bit better. I would think that cooperation between home and school on a specific plan of action might be helpful; for example, a verbal reminder from the teacher about which assignments to bring home, checking his agenda to make sure things are written down, you checking his stuff when he walks in the door, and then again the next day to make sure the stuff is in his bag...and teacher asking him specifically for it. I'm betting he will NOT like the extra "attention" and if he is able (i.e. if he has no issues like ADD, etc) he will soon start taking care of this, if only to stop teacher saying "X, do you have your science?"
My DS has a locker that looks like a tornado hit it...every once in a while I will go pick him up after school and make him clean it out. He still loses things but with both sides on top of it things are progressing!
I might suggest an IEP for him that stresses organizational skills also.
NotUrsula, it's unfortunate with the $$ you are handing over to the school, that they can't be more helpful than brushing the problem aside. Your DS obviously needs assistance, especially with the Asperger's making things even more difficult. They are not doing him any favours by saying "sorry, it's his problem." I'd be at the end of my road with that sort of "cooperation"...