I think honestly the problem isn't so much always with tragic endings, it's with unfulfilling or unsatisfying -- or plainly inappropriate -- endings.
Tragedy can work, but it's done to death (no pun intended) and usually not as well as people would like to think they're doing. Lots of people think they do tragedy well, or that they can do it even if they've seen it done a thousand times poorly, but that's often not the case. It's tempting to try tragedy because some believe it makes a story "serious" or "legitimate" somehow to be tragic, but tragedy is more than sad things happening and a downbeat ending. Many writers simply don't understand what tragedy means or how to use it well. As a result, there's a lot of flimsy tragedy out there that has soured a lot of people on the approach, and it's much easier to sour an audience on tragedy than it is on comedy or lighter fare; a far greater emotional investment is asked for tragedy, and it's repaid in sorrow. It's necessarily emotionally manipulative, and that's playing with fire since the strong negative emotions can be blurred in relation to the story evoking them.
Additionally, a bad ending can ruin an otherwise good story. If the ending doesn't fit the story, or if it's just trying to be downbeat for its own sake, or is inconsistent with the previous tone, it may be worth reconsidering and approaching differently. A sad or downbeat ending isn't necessarily bad, though. It is harder to do one of those than it is a happy ending or an ending that is neither happy nor sad, or even an open ending. But at least make it fit the story and satisfy at least mostly. Or give the audience a "jumping-off point" before the real haul to the end. Many stories make the mistake of tying in the "ambitious" lead-up to the end to everything before and, as a result, if a reader really dislikes the ending and its storyline, they end up linking it to all the rest of the series and dropping it like it's hot. If a reader has somewhere to stop that they remember, they don't have to read the ending they disliked and can just imagine it any way they please.
Ultimately a lot of endings just aren't satisfying because, when one gets right down to it, if you've done it right, the audiences probably shouldn't want the story to end, per se.
But I think perhaps the best example here would be the Chronicles of Narnia. Most who have read the series enjoy the all the books until they reach The Last Battle -- the final book in the series -- where Lewis apparently threw away his aversion to attempts at allegory and went absolutely insane, which is a shame because The Magician's Nephew, the penultimate book, tends to be the best-regarded of the series. However, as the only really poor entry in the books, it's easy to simply avoid The Last Battle since it's self-contained; the story before it isn't in chronological order, and it's easy to read The Magician's Nephew and close the book on Narnia on a high note. Because The Last Battle is by no means required reading (and doesn't flow particularly well with the previous story), it's easy for audiences that don't care for it to simply have their stopping point at the end of The Magician's Nephew and have a satisfying point of closure.
I think the long and short of it is: a tragedy should still have a satisfying ending that is consistent with the story that came before; and, give your audience a point of some closure where they can return to if they want to read it again, before you really get things in final approach to your ending.