Oh yeah, it happens to me. Especially with anime.
Usually it's more rage induced though.
Case in point:
Evangellion. After watching the end of the series, and I quote, "What the fuck was that!?"
So then I watch the first movie on my friend's recommendation. Something about making sense of it all. My response? "What the fuck was that!?"
So then he admits it was a joke, har har. The second one actually gives a proper resolution to the plot. Me? "What the fuck was that?"
Elfen Leid. Wait. What? He want's to bone his relative? What? I mean, never mind that the anime basically gave the manga it's based on the middle finger and deviates from the plot line, it threw in shameless fan service, created a moronic split personality character and does shit to actually do anything.
Soul Eater. Ok, I'll give it leeway purely because they had to break out the crystal balls and see into the future and end it so that it'd wrap up the plot lines without actually knowing where the manga goes. Incidentally the ending was forgettable, and generally just plain bad. It's not as bad as what's above but it's still a situation where I want that hour or two of my life back, k?
Ghost in the Shell gave me a bad migrane, but I don't know if that counts as "depression" so much as "What the fuck did I just watch?"
But yeah, at a basic level its only natural to at least feel something when something you follow is suddenly taken down. Well, maybe not suddenly. Humans like to prattle on about how change is good and nothing is constant, but far from it, we aim very much to sink into a system of sameness. It's comfortable. We like taking an hour or so once a week to keep up with that one TV show. For whatever reason it's enjoyable to watch someone else going through the same motions we are. Kind of.
You'd have problems if your favorite show ended and you felt nothing.