Hi! I'm a teacher, so I'll tell you what I know about the Special Ed system in public schools:
If you request testing, they HAVE to comply. This will be at no cost to you, and if they discover that he is indeed learning disabled, the district MUST work with you to devise an Individualized Education Plan (IEP) for your son that EVERY teacher he has must follow. It will include accommodations (like sitting close to the teacher, frequent repetition of directions, extra eye contact, a special assignment sheet, etc.) and modifications (actual lowering of mastery expectations) as needed.
HOWEVER, it sounds as though your son has been shafted by the system...someone wasn't doing their job, and now they're expecting him to be held back 2 grade levels when he's already been held back one?? That seems to indicate that they've been dropping the ball for some time. It's true, it costs the school system money to test these kids, and it's also true that the disricts push the Special Ed departments not to have too many kids in SPED, otherwise they have to hire more people to monitor. So, here's what you may want to consider instead...
As the other moms suggested, have him tested at Scottish Rite. They specialize in the needs of children, and can pinpoint problems that a general hospital could not. They are the best with diagnosis. They will not fail you. But you have to be willing to sink quite a bit of money into the testing, and you should know that it won't be a one-time thing. You'll probably have to take him regularly for a while, as the tests don't usually take place all at once.
Once he has been diagnosed, which it sounds like he probably will be, I would recommend getting him into a private school for learning disabled kids. He obviously has been ignored by the public school system, and a school that caters to learning disabilities can teach him how to manage his disabilty and give him the tools to be successful in the future, whether he's being catered to or not. I don't know where you live, but you should look up The Shelton School in Dallas. They have a great reputation, and I've had students come into the mainstream school system after having been there during elementary. They were well equipped with knowledge of their disability and the tools to cater to their own needs. They still had to have modifications and accommodations, but they were successful, and that was important. Their website is shelton.org. If you can't afford a private school, then it's up to you to become his advocate. Educate yourself on his disability, and then go to bat when he needs you. Be at every ARD (Admissions Review and Dismissal) meeting, know what's going on, and be willing to stand up for what you know is best for your child. If he needs to be held back, consider putting him in a different school where he might get a fresh start, socially.
The bottom line: knowledge is power. Once you know what's wrong with him, you can get educated about it and move forward. Until you know, you won't be able to do anything. Get him tested, and do it as soon as possible, otherwise you'll just be standing still, and he'll be getting farther and farther behind. Best wishes to you and your family. Please let us all know how it all works out. I think there are plenty of parents who are in the same situation as you and simply don't know what to do. The more awareness we create, the fewer kids will fall through the cracks. Good luck!