I was thinking about the level of excitement that fans can get over authors unfinished works, specifically the way some of George R.R. Martin's fans chastise him for not working fast enough and openly talking about the possibility of him dying before finishing. I know they are very different types of books. Did some of Marx’s readers feel he was not spending enough effort on writing his work, and was his health a discussed topic in regards to completing Das Kapital?
Marx was never a blockbuster author; for most of his life his 'supporters' were a collection of personal friends and radicals on the fringes of Europeans politics. That didn't really begin to change until the first mass worker parties began to emerge in the late 1870s (particularly the SPD in Germany, although Marx's relationship with its founders was ambiguous). It wasn't until after his death that you get what we would consider 'Marxist' parties*. So he certainly wasn't writing to the sort of audiences that GRR Martin enjoys and there wasn't the same pressure to produce a follow-up.
But then Das Kapital is not, and was not intended to be, an overly political work. What ticked Marx off the most about its reception was that it was initially ignored by the professional economists and critics, whom he complained tried 'to kill [the book] with silence'. So it wasn't until the mid-1870s that it made any real impact and non-German translations began to appear. Even then the reaction was muted towards what was a pretty dense work of economic critique. (Ironically, the exception was Russia where the book was a relative hit from its publication in 1872.)
So Marx wasn't the sort of writer who had an eager following and Kapital wasn't the sort of book to inspire excitement over sequels. It's influence has grown massively with time, particularly with the later development of explicitly Marxist political movements, but it wasn't a massive success or landmark in Marx's lifetime.
Just as an aside on health, towards his final years Marx's health deteriorated sharply. From 1873 his capacity for work was much reduced by a series of recurring ailments (most obviously liver trouble and depression) and the grind of a penniless existence (including caring for sick wife and child) wore him down. It took twenty years and immense effort to get Volume I of Kapital published, he was never likely to be able to deliver on the following two.
*In contrast, Engels outlived Marx by a good decade and did become very much involved in the development of Marxism as a political ideology.
Sources: For Marx himself, Nicolaievsky's biography (Marx: Man and Fighter) is a good place to start. The publication history/reception of Kapital is from the introduction of my edition of the book, by Roberto Marchionatti. And while I've not read it (hence it's not really a source) I've heard that Francis Wheen's Das Kapital: A Biography is a decent read.