Update: spoilers in the comments on this post.
I didn't realize when I watched my first episode a few weeks ago that it's such a cult hit. I think the "yearning for a simpler time" bit is silly. What's simple about it? A very different time and culture, yes, but yet not so different as to be incomprehensible. But its main appeal is just that of good old soap-opera and costume drama, and the standby of all popular drama, interesting characters in interesting situations.
I meant to mention, when I wrote about it earlier, the way Maggie Smith, as the Dowager Countess, steals every scene she's in. The character is so over-the-top in her commanding bitchy snobbishness, and yet you like her anyway, especially as she occasionally reveals a kind heart. My favorite remark of hers occurs when she's told that two estranged sweethearts are coming to the Abbey for a visit, "but don't worry, they aren't on the same train." The Countess reacts with a somewhat over-enthusiastic expression of relief, then, slightly embarrassed, replies to the quizzical looks with: "I do dislike Greek drama, where everything happens off-stage."
Here's a selection of clips that will give you the general idea (if you haven't been watching):