Typically? No, not really. Most of the shows where something comes to a close that has characters I really enjoyed or cared for (read: really was interested in the development of the character itself and their purpose in the plot) I feel things coming to an end means at least that character's conflict has finally come to an end and they can (hopefully) feel at peace.
Even Air TV, which is without a doubt an anime with an incredibly bittersweet and painful ending, has a sort of 'relief' once it finally comes to an end. Everyone's reached a conclusion and everything is 'resolved' for the most part. It leaves on a very slightly vague ending but the central plot is concluded and any further speculation doesn't hurt the primary product of the show itself.
The same can be said for products from the same creators, specifically Clannad and even Plane- Oh right, that doesn't have an anime yet, nevermind.
Code Geass ends on a similar 'all the central characters plots are concluded' ending, so I consider it another successful project as well.
In all honesty, there are rarely shows where I see a character I like so much that I want it to just keep going on forever. More often, I fear a character not getting a finite conclusion.
To use a non-anime example, recently a favorite series of mine, In Treatment, concluded its third season last week. The main character within the show is one that is, in a way, tormented by his work and has never, IMHO, truly received a sense of peace or happiness since the series began. He's not an UNBEARABLE tragedy, but a painful one without a doubt. He's be used, felt helpless, tormented by others, the list goes on for the sort of things Paul Weston's.
The problem with this is that (and fair warning now, if you haven't seen the ending for his sessions with Adele, don't scroll any further) things left on a vague premise where Paul's considered closing up shop and ending his practice because he feels like he's not going anywhere with it. He's 57, potentially has Parkinson's and feels like he's got nothing to live for and he's considering just stopping his work, figuring that (from what I interpreted) if he feels like he has nothing to live for (granted, he's not suicidal) he shouldn't be working to help other people figure out their inner conflicts and problems.
For me, I would HATE to see Paul never get the 'happiness' he deserves in the end. He's a kind hearted person who clearly cares about what troubles his patients and tries his hardest to help them. And ESPECIALLY considering that 2 out of his 3 patients from this season either used him or abandoned 'working' with him, the reasoning behind his ending his practice is significantly justified.
But as a fan, I just would hate for that to happen. So, I'm hoping for at LEAST one more season, where maybe somehow he finally finds a sense of satisfaction or maybe someone to love so he can either close his practice on a positive note or use that person to be a driving motivation to go on and keep working.
I'm crossing my fingers though that we'll get a fourth season.
tl;dr Short series are good and if characters are properly developed and have their conflicts resolved properly, it makes the 'parting' with that character that much less painful and more pleasant to the viewer. Anime, TV, movies, books, games, w/e, it applies for all media outlets.
