For me, that is. These things are extremely subjective.
Villains usually come with an inbuilt expiration date when we're talking about tv shows. Especially if their objective is to destroy the hero; they can try only so often before losing all credibility as a genuine threat. Also, if you compensate by letting them destroy everyone else but the hero, the hero starts to look bad and incompetent for not being able to contain them. So, given you don't want to kill your villain off after one story, what do you do? Here are some solutions tv shows of ages past came up with that worked for me. They all could be summed up with: "Change the agenda from "destroy the hero" or don't give the villain that agenda to begin with, but do give him an agenda which puts him/her at odds with the hero".
That's what Farscape did. The original villain early on in the show was Bialar Crais, who started out as your standard arch nemesis; he hated our hero, John Crichton, because Crichton accidentally got Crais' brother killed in the pilot, was immune to all attempts at pointing out this had been an accident, and did all manner of crazy and villainous things in pursuit of Crichton and the rest of Our Heroes. This, you'd think, does not leave much room for development other to kill off Crais after some final confrontation, but no. Near the end of s1, the show not only introduced a new villain - more about him in a moment - but took Crais in a new direction. They didn't do this by suddenly negating the villainous things Crais had done so far, or letting him reform immediately. He basically lost everything he had defined himself through - partly through the new villain, but mostly because of his own previous behaviour - and then, during a brief alliance of necessity with our heroes, had a shot at escaping (leaving our lot in the lurch), and took it. This also gave him responsibility for what was basically a child and a weapon at the same time, and this bond, in turn, changed him. It didn't happen overnight, but it happened, and Crais went from villain to ambiguous character with uncertain loyalties to tragic hero. Even the manner of his death, though, wasn't completely "white" but shades of grey; on the one hand, it was a sacrifice, but on the other, it was also a final act of revenge. Against Scorpius, who of course was the character taking over the top villain job from Crais at the end of s1.
Scorpius from the start was a different type of villain. He wasn't interested in killing Crichton (or the rest of Our Heroes), on the contrary. He was interested in the knowledge that Crichton, due to other plot developments, possessed, and this in turn was because Scorpius' main goal in life at that point was two-fold: a) destroy the Scarrans, and b) save the Sebaceans. With it being an open question which of these two was more important to him. But he thought he could accomplish both through the wormhole knowledge in Crichton's head. This allowed for a different type of story to unfold than the early s1 "Crais chases, Crichton & Co. escape" ones. It also meant that as opposed to Crais, Scorpius didn't have something resembling a redemption arc. Being a villain of the "everyone is the hero of his own story" type, i.e. someone whose methods and agenda are at odds with those of Our Hero, which results in conflict, but whose goal isn't by itself selfish or lunatic, he didn't need to. He didn't have to be killed off, either. While there were some missteps with Scorpius in s4 (to wit, the writers for a while didn't seem to know what to do with him anymore once he was out of power), his story was ultimately resolved, as much as anything in Farscape ever was, in a surprising and yet appropriate way: through the Scarran/Sebacean peace with Scorpius, the child of both races, brought into the world through rape and raised through violence and torture, appointed to make sure both races kept to their bargain. This was possible because Scorpius' obsession with Crichton had been powerful but secondary to his main goal, and so a compromise could be reached, and Farscape's main villain actually got a happy ending.
Another example of a recurring villain who was kept around for encores in a credible fashion was Alfred Bester in Babylon 5, and the reasons this worked was similar to the ones I just named for Scorpius in Farscape. It's also worth comparing the way Bester was written to some of the other B5 villains. The main antagonists from the end of s1 to the middle of s4 were the Shadows, but they weren't individuals. Their human representative, Morden, was, but there was nothing whatsoever ambiguous about Morden, and as his agenda was identical to the Shadows, he left the stage, so to speak, the moment the Shadow arc ended. He had no further purpose on the show. (Save for one encore to mess with someone's mind, but that was a strictly limited thing; the character himself remained dead and gone.) We also had the dangerous lunatic (which neither Morden nor the Shadows were) type of villain in Emperor Cartagia, but again, Cartagia had a limited life. Though he's referred to from mid s2 onwards, he only shows up on screen in s4 and gets killed off; he's not someone who could have credibly remained around. And lastly, we had the greedy (but sane) powermonger type of villain, which would describe both the largely off screen President Clark and Londo's temporary ally and later enemy Lord Refa. (Londo himself is a case of his own, as he spends one season seeming to be the comic relief, two seasons doing largely villainous things and two seasons as a tragic hero.) Again, all of these bite the dust sooner or later. So how come Bester does not, without this impairing the story?
For starters, JMS changed the "Bester visits station, causes trouble, gets defeated by Our Heroes" formula with Bester's third appearance, which is also the first one where our Psi Cop a) gains some layers, b) has a temporary alliance with Our Heroes and c) actually gets what he wants out of the situation of the day. Bester throughout five seasons never stops being a fascist, as Sheridan once calls him; he also is presented a sincere believer in the idea of all telepaths as a family (with some misguided members who must be brought back to the fold), and given a number of qualities that make him interesting; in addition to being a ruthless bastard, he's courageous, not afraid to risk his own life repeatedly for what he believes in, relentlessly witty, capable of attachment and flexible enough to compromise if he has to. Also, his main agenda (telepaths ruling the world) isn't compatible with the Shadows' agenda, which creates believable situations of a temporary alliance without letting Bester see the error of his ways first, and it also allows for him to remain a threat to Our Heroes after, because if his agenda isn't compatible with the main antagonists, it's not compatible with theirs, either. At one point in the later seasons, Bester tells one of the good guys sardonically "believe it or not, not everything in my life is about Babylon 5", and he's telling the truth, but one of the show's most effective twists is that the very fact Bester isn't obsessed with the B5 gang doesn't mean he's less dangerous to them. One of Bester's ploys in season 4 gets Sheridan, the closest thing the show has to a leading man and main hero, captured by the bad guys, and yet he couldn't care less if Sheridan lives or dies; this was just one of the means to an end which has nothing to do with Sheridan at all and everything with finding out about a weapon which could wipe out or control telepaths.
To return to the beginning: the best ingredient for keeping villains around without turning this viewer off seems to be through giving said villains goals which extend beyond "must crush hero", or, if said villain originally has this goal, to give them something else along the way. Most importantly, though: their villainous deeds must never, ever be prettified, retconned or excused.