From your own user handle, I assume that this subordinate works as a software developer. 

> I feel like I have to walk on eggshells, as part of the reasonable
> adjustments put in place already I can't Skype my subordinate when he
> works from home, I have to e-mail him, but he then ignores his
> e-mails. So I have no idea what he is doing or why his work is taking
> so long.
> 
> Having sat with him before his health conditions were disclosed to me,
> I found he was not able to focus on what he was doing and that he
> often sat staring at his screen for long durations of time doing
> nothing.

A software developer, who is not able to focus on his work and who stares at his screen all day, **doesn't need less structure, he needs MORE structure** (At least, according to my lay opinion). 

In other words, I believe he needs shorter feedback loops, and things like daily stand-ups, less social isolation, more face-to-face meetings, more pair programming opportunities, code reviews (not just his code review, everyone's code), screen-sharing turned on automatically when he's working remotely (like oDesk/Upworkd did/does for its work diaries. See [pdf][1].), etc. 

Now, I am not a lawyer, nor do I work in HR either. So take everything I say with a grain of salt. And nor do I know what that health condition is (and for privacy reasons, I'm not going to pry). 

But in my opinion:

1. When a company is "required to make [reasonable][2] accommodations", it doesn't mean that the employee unilaterally gets to decide what those accommodations are going to be. After all, the employee himself, while being an expert on his own health condition, may also be the totally wrong person to make that kind of decision for himself. 

2. Everything I've said about needing more **structure** could be wrong, but I wouldn't necessarily trust the opinion of an HR professional either, and I would want the company to seek the input of a 3rd party health professional specializing in that condition as well. 

3. If a disabled employee can't work reliably on a full-time schedule, then one accommodation may be to make that employee a part-time employee instead of a full-time one and perhaps use the extra money saved to hire someone else part-time as well (after consulting with a health professional and legal counsel obviously!!). 

4. If the accommodations go beyond being "reasonable", then it may make sense to seek legal counsel and fire that employee if he doesn't improve (again, diligently following the advice given by your legal counsel!).

5. Placing the entire burden on you to both oversee his work, and the extra work that requires, and make up for his share of the work is also unfair to you. If you do this extra work at home and bear that cost yourself, that may make the consequences of the problem invisible to your employer (and to your HR person as well). This is a burden for the entire company to bear, not just you. Even if you can't get the particular resolution you're hoping for, you still need to advocate for your own needs so you don't burn yourself out. Either that or you may want to consider looking for better employment elsewhere.


  [1]: http://mba.danielwatrous.com/wp-content/uploads/2013/08/ethnographic-study-odesk.pdf
  [2]: https://www.eeoc.gov/facts/ada17.html