[Boromir88]

Ah, but I didn't commit myself fully there. I stated that he lacked either the time or the inclination to explain everything away. You make a good case for him having the time available, so that leaves only the inclination.~Doug

I think you can even make a case for both. Probably earlier on in his life he had time to spend and work on everything. However, as he got older it seemed like he got rather bogged down with trying to 'answer' everything, saying that everybody wanted an answer for something. Also, as he got older his health began to decline. So, I think you can make a case for both. Here are a few related quotes:

... while many like you demand maps, others wish for geological indications rather than places; many want Elvish grammars, phonologies, and specimens; some want metrics and prosodies.... Musicians want tunes, and musical notation; archaeologists want ceramics and metallurgy; botanists want a more accurate description of the mallorn, of elanor, niphredil, alfirin, mallos, and symbelmynë, historians want more details about the social and political structure of Gondor; general enquirers want information about the Wainriders, the Harad, Dwarvish origins, the Dead Men, the Beornings, and the missing two wizards (out of five).~Letter to H. Cotton Minchin

I don't think he ever lost a love for his books, but I do sense that he did get bogged down (and even tired) with consistently trying to answer everyone's questions about it. Compile that upon with his declining health. Consistently through Letters he responds with being 'sorry' for answering so late but his health didn't permit it...here are just a few:

I am sorry for the long delay, I was unwell for some time, and then faced by a family laid low one by one by influenza.~Letter #9

I have been unwell since I last saw you – in fact I reached the edge of a breakdown, and was ordered by the doctor to stop short. I have done nothing for a week or two – being in fact quite unable.~Letter #33

I have worked under difficulties of all kinds, including ill-health.~Letter #35

These are all around the age of when Tolkien was in his fourties, and by much later his health gets dramatically worse:

I am (temporarily, I hope) deprived of the use of my right hand and arm….~Letter #245

I have been ill, and am still suffering from rheumatism in my right arm…~Letter #247

His publishers Rayner Unwin and George Allen also noticed the health of his wife may have contributed to part of the problem:

Even more distracting was the declining health of his wife….It was Edith’s ill-health that precipitated their move from Holywell to the ‘high dry soil’ of Headington in 1953, and later in 1968 to Bournemouth. But even there arthritis and other illnesses continued to afflict her. She was in hospital in 1958. Soon after coming out she broke her arm, and two years later she was back in hospital again~Allen & Unwin A Rememberence Chapter

With all that being said. I don't necessarily think that him not finishing things was completely due to a lack of time, or a lack of inclination. I do see what Mithadan is saying in that I think some things he left purposefully unanswered to put out in the public and see how the public viewed his books:

Practically speaking of course, none of the Matter of Middle-earth was ';finished'; but continued to evolve, and was open to second thoughts while Tolkien lived.~The Development of Tolkien's Legendarium

Of course the L.R. does not belong to me. It has been brought forth and must now go its appointed way in the world, though naturally I take a deep interest in its fortunes , as a person would of a child.~Letter #328

So, there definitely seems to be not just one specific defined answer, but several. Some things he wanted to purposefully leave unanswered (I think perhaps Tom Bombadil is the best example). Also, there were the problems of his health which contributed to a lack of time and a lack of inclination.