Performance managing staff suffering from stress/depression (UK)

 Would it be possible for and Occupational Health assessment on your manager?
This could then let you know where you stand?

I'd like more input from Mike and Mark on this.  I've seen or been involved with a lot of situations like this where the direct's performance is passable sometimes, but often below standard, and rarely consistent.  This is usually accompanied by emotional issues or problems at home, which makes the manager look evil if they try to hold the direct to a higher standard.  What are some keys to handling this well?  Are there podcasts that would help?

I cannot really tell you what you should do in this situation.  All I can do is share with you how I felt being in sort of a similar situation to that of your direct and how my manager acted on the situation and how it helped me.
Earlier 2011 I faced a very difficult personal situation at home in part caused by overworking and relying too much on maids to look after my kids (4 and 2 year olds).  That in turn lead to insatisfaction at work which in turn led to poor performance.  Before I could actually cause too much damage in my career and in my relationship with my boss and peers at work (and to my family), I physically collapsed and ended up at the emergency room with a anxiety attach.  I then told my manager about the difficulties I was facing and he told me to stay home, take all the time I needed to get things in order and come back when I could.  I got back to work after 3 months off and started, and still am, working part time.  I cut down my salary and my responsibilities.  Right now I am building up again on the responsibilities and i may need to adjust the working time a bit.
The adjustment has not been easy for me and I believe also not easy for my boss, as we both need to constantly evaluate what responsibilities I can take in with the less working hours I have.  It has been better though (both for me and for my company) than the other option which would be for me to quit completely.  
Two things have been key for me to maintain (or regain) performance:
1 - the unconditional trust from my boss into my work.  I once actually told him I felt I was loosing points with him.  He answer back that that was ok, that I had accumulated lots I could loose some.  That for me was very important, because just as I looked at the history I had with the company and on the long term future perspective as well, he did the same with regards to my work.  Or put it differently, the thought that I was allowed to fail kept me from failing because I could focus on the job at hand rather than worrying about whether I would perform sufficiently well or not.  The sentence "people and family first" was a reality, and not just something nice to put on the papers but not really act upon it.
2 - the establishment of clear objetives, targets and accountability with respect to the ones agreed upon.
Now, how does that story relate to the situation you are facing?  I can only guess.  By drawing some analogies between your story and mine I can risk saying, and please filter it as you wish, as I am basing my analysis on my case and the very little you wrote about yours:
a) When you say that "From my perspective, he's being paid at a salary level and rank which he no longer really deserves, but I'm worried if I push him too hard to perform he'll have another lengthy sick leave."  You don´t really know if today he is being paid a salary and rank he no longer deserves.  He probably received a higher salary for a while when he was not performing.  But you must leave the past in the past and give him the chance to perhaps surprise you?  And somehow either you made a mistake on giving him a promotion, or he really deserved it.  So do take the longer past, before he actually decreased in performance, into consideration as well. And truly give him a chance to perform again.
b) Regarding you worrying about pushing him too hard to perform, at least in my case I didn´t leave because I was pushed too hard, my difficulties in coping with family and work load were a result from not having very clear bondaries on what was expected of me at work and not having a clear measurement of how well I was doing.  So I was just over trying with very little satisfaction from trying, and perhaps not trying in the right things.  Analyse your situation critically, perhaps your directs team was getting far more projects than they could actually handle before he collapsed from stress, on the top of that, your direct had the expectation that he would get a promotion which he didn´t.  That combination of too much work with unmet expectations of the work performed is actually what drives one to stress burnout.
The 12 questions from the Measuring Stick for the strength of a work place from the book First Break All the Rules have become my personal measuring stick.  The number was really low before I almost burnout and right now is a lot lot higher:
1 - Do I know what is expected of me at work?
2 - Do I have the materials and equipment I need to do my work right?
3 - At work, do I have the opportunity to do what I do best every day?
4 - In the last 7 days, have I received recognition or praise for doing good work?
5 - Does my supervisor, or someone at work, seem to care about me as a person?
6 - Is there someone at work who encourages my development?
7 - At work, do my opinions seem to count?
8 - Does the mission/purpose of my company make me feel my job is important?
9 - Are my co-workers committed to doing quality work?
10 - Do I have a best friend at work?
11 - In the last 6 months, has someone at work talked to me about my progress?
12 - This last year, have I had opportunities at work to learn and grow?
Good luck both for you and for your direct.  It is not going to be easy for neither one of you, but if you can both work on the same basis and if that basis is built on trust and honesty you can definitely succeed, and by succeed I mean getting the results you, and I am sure your direct also, want from his work. 
Nara