Other times it can be the best thing to happen to some strips. Case in point:
It's Walky. For about the first year or two of its lifetime it was your average, run-of-the-mill webcomic made by a college student about college, and then the creator suddenly decided to interject some seriousness into the strip. It surprised me at first, I re-read the strip when the first death happened trying to find the dark humor in the situation but saw nothing. Intrigued and a little confused as to where that came from, I kept reading and found that it began to develop into its own continuous storyline which went back and forth from light-hearted to serious that was well beyond what it started with.
I haven't read it in probably about a year now so I don't even recall how good it actually was, but an ongoing story can make an alright comic into a good one.
(I found that comic and a few others a couple years ago when I was bored and was reading all the archives of Keenspot comics I could find to weed out the interesting ones.)