I have to ditto what Marg said about hard work and no idle time. While my difficult children were different in approach, focus and retention were always an issue. difficult child 2 assumed he could easily absorb everything (because he excelled so much in academics) and therefore wouldn't pay attention. He stopped retaining information and was hard to redirect to tasks he found uninteresting. I couldn't tell you how many times I heard "But I already read/did/finished that," yet he couldn't tell me anything about it, or repeat the process again on his own, which meant he didn't retain it. It was working here on the farm that really provided an answer for difficult child 2 in that regard. I hate to say it, but he was a lot like training a stubborn horse.
With a horse who is resistant to following directions/staying focused/retaining newly trained skills, often the trick is to keep them moving. For example, my last Quarter Horse, Smokey, would stop walking and listening to cues. He'd go off in his own direction, no matter how I pulled at his reins or signaled him to turn around. I couldn't tell you how many times I had that horse's nose to his hind quarters, turning circles in the dirt, simply to remind him that he either stayed on task or I would force him to do the most mundane walking in circles junk. If all else failed, I'd lunge him and sweat the lack of focus out of him. (Lunging a horse is having them run laps inside a training ring, stepping in front of their path at a controlled distance to force them to turn away and go the other direction, over and over and over again. It does wonders to gain their attention and focus, especially if you plan to try something new and need them to retain it.)
On the trail, you learn to notice hints and cues that the horse is losing focus and might turn off on his own. You take steps to bring their focus back, before they actually need redirection. That might be something as simple as upping the pace, turning a few steps off the trail, whatever it takes to keep them focused and forced to keep moving. Our trainer always told me, keep him moving where YOU want to go, don't ever let him have a chance to think about where HE wants to go.
Amazingly enough, the same concepted worked with difficult child 2. (Is is horrible that I used the same techniques on him as I did on our animals? lol) I learned that if I got him as soon as his feet hit the floor in the morning, before his brain woke up and said "I don't wanna" and kept him moving and doing, he stayed more focused - even on things he really wasn't interested in doing. That meant getting him up and on his chores first thing in the morning, then getting him out the door for outside work, often doing school work verbally while we shoveled gravel into the bed of the truck, or split wood, or whatever needed doing. (There were times I had him doing things that really didn't "need" doing, just to keep him moving and in a "working" mindset.) He stayed busy enough that he didn't have time to think about what he wanted to do. His time came later in the day, after he finished what he needed to do.
I know that can be hard, given your educational options at the moment. However, even little changes to keep him always "moving" can help. Apprenticeships are great for that kind of thing, especially if its someone he respects. With both of my difficult children, I've found that the instant reward of completing a physically challenging task carried over to less physical things. I worked right beside them, and was just as "unhappy" about a demanding chore as they were, but we all kept working with the "lets just get this finished so we can move on" mentality. Let's just get this last truckload shoveled. Then it was, well, we can do one more, there's not much left. When we were done, they were surprisingly proud of themselves for pushing through. It took awhile, but eventually difficult child 2 started to have that same mentality about schoolwork. He didn't want to pay attention, but he had learned with physical labor pushing through got it over sooner, so he started pushing through school work, household chores, etc. But he still needs his own form of lunging first thing in the morning to get his focus on track and put him in a "working" mindset. The only difference now is it only takes a verbal reminder like "take out the trash when you're done with breakfast" to get him into work mode.
I know our situation is different because we were able to homeschool and thus take matters into our own hands to find a solution, but perhaps finding a volunteer spot or other option could, over time, help him with self discipline and focusing on the task enough to retain something - even if only in tiny bits and pieces. It certainly couldn't hurt to try. I'm continually amazed by the seemingly unrelated things that somehow trip a lightswitch somewhere in difficult child 2's head. Try looking at his daily routine, from eye opening to snoring again, see if you can't find ways to apply the "keep him moving, keep him working" idea. It might help, it might not. It will take more than a few days, weeks, perhaps even more than a few months to see a real difference, but it's something to think about.
I know with difficult child 2, when it came to schoolwork, our verbal conversations about it while working on a physical task often garnered better results than sitting a table with him. It gave his mind something to do while his body was working on something else. Kind of a "well, it's something to talk about so I'm not thinking about how tired this is making me" approach. "Casual" conversation about his schoolwork while working on other stuff seemed to "stick" in his mind moreso than traditional, sit down at the kitchen table and do homework approach. When we were done physically working, sometimes he'd stand at the bed of the truck and write out his math problems, or answer his science questions, before we moved on to something else - while the information was still fresh in his mind.
