Consider the TV show House. Unquestionably, House's private life is strewn with disasters in the offing, but there's never a sense that they're inevitable; one can also hope for positive outcomes and they do sometimes come. And not merely "just enough to temporarily stave off catastrophe", but genuine positive turns. In any case, the bad things in his private life are backdrop and backstory: they both demonstrate and explain the real star of the show, his irascible, curmudgeonly ways, his knack for saying what no one else can get away with saying. Plus the medical Sherlock Holmes story.
Contrast the show Nurse Jackie (which I don't watch, but I am often in the room while Siobhan watches it). The overall theme of that show is that a mostly-unlikeable (though with a few redeeming moments) character starts out on the path to imminent catastrophe, and just barely averts the worst happening. Over and over, though while still conveying a sense that it's always nearer than ever. And that's about all. She's as unlikeable as House in the sense that you wouldn't want to be her friend, but from a safe distance (the other side of a TV screen) House is likeable to watch, but not so Jackie. We're not watching her, we're watching the inevitable disaster looming towards her. That disaster is what the show is about.
I don't mean to pick on Nurse Jackie but just to use that show as a contrast to House (since they're both also medical shows). It seems as if this is the formula by which those TV shows that run on cable channels are made: unlikeable characters largely devoid of redeeming qualities, even the "always right" quality that almost justifies some of House's prickliness, with whom we sympathize only to the extent that we worry about the catastrophe they are hurtling (intentionally or not) towards. The United States of Tara is another good example: while that at least has another story (Tara figuring out why she is like she is), most of it seems to be watching the train almost go off the rails and wondering if they'll survive another day.
Even Dexter, which I do watch and enjoy a lot, uses this quite a great deal. Dexter is about a lot more than the imminent disaster that haunts him, but that is unquestionably a plot element that they play with, and have built whole seasons around. Though one big difference there: at the end of the season, when by some miraculous chain of events Dexter dodges the disaster, it's resolved. When Nurse Jackie avoids her life of lies falling to tatters today, the same threat hangs over her head tomorrow, and not even in a really new form.
Generally speaking, throwing your characters into peril and watching them narrowly escape is of course a part of almost all fiction, and has been around forever, and there's nothing wrong with it. What's key to this pattern is that that's pretty much all the show is about. It's that moment of falling off the cliff, barely catching yourself, and then a few seconds to set up the next fall, and repeat. The only reason you care about the character is that she's falling off the cliff and you would probably rather she didn't, but otherwise, you wouldn't give her a second thought; and if she did fall off, you'd figure she deserved it, too, so it wouldn't be too bad. It's like eating a big bowl of spices, without anything for them to be spicing.
Was there some greatly successful show that set the standard of watching characters plunge off the rails as a form of entertainment, explaining this trend?