Note: Don't attach this concept to issues since it's highly opinionated.
The term "jumping the shark" came from a Happy Days episode in which the Fonz, while water skiing, had to jump over a shark. Many viewers found it illogical to Fonz's character and rather stupid. People were also finding that the quality of the shows after that were in a decline. In order for something to be jumping the shark in any medium, there has to be something specific that happens in the series that watermarks (get it?) the end of that series being good. People are usually forever changed as to their opinions of that series afterwards. It isn't "jumping the shark" if the series slowly declines and nobody can put a finger on it as to why it's that way, nor is it if the series has a bad episode, but with good episodes after it, and the bad episode is forgiven.
Like any serial medium, comics is rife with opportunity for jumping the shark. Listed are certain ways that a comic series that jumps the shark. These reasons aren't exclusive, sometimes, it's more than one factor which makes the title jump the shark.
Artists/writers leaving or introduction of new writers or artists. Sometimes a series has a fantastic team: great writing, great artwork, etc. Then suddenly someone new comes in, and that series is on a one way trip to Sucksburg. Or sometimes there's a team of artists or writers, and someone leaves that team (and nobody replaces them) and it's apparent where the talent was. Within a few issues a comic can go from awesome to so bad, you wonder how the ink stays on the paper.
A character entering or leaving the series. Since comics are character driven, they are very important to the story. Sometimes changing the formula as to who is in or out of the storyline can be disastrous. Characters can leave the series for many reasons like death or disagreement with other characters. The character leaving can make the comic bad, especially if he is a fan favorite or about the only thing holding the series together. For introducing a character, the character usually has to be nonfitting to the story, irritating or otherwise make the comic unreadable (boring characters introduced are usually just ignored and aren't usually jump the sharkworthy). Sometimes it's not the hero characters, but the villain characters that are bad (not just evil). People want this usually shoehorned in character to die soon and painfully. One of the most famous examples (although this is a cartoon) is Scrappy Doo.
The plot becomes absurd, silly, stupid, etc. A lot of times, the people behind the comic want to take the comic in a new direction. The problem is it's a bad direction. Or they used their good ideas up first, so now its time for the not so good ideas. Sometimes they paint themselves in corners, and judging from what they're doing, they've been sniffing the fumes. Although there may not be a specific panel that people can draw on and say "everything before this panel was good, everything after this panel was bad," when a story arc is mentioned only in angry or dejected or "those were the good days and this isn't" tones, that comic may have jumped the shark.
They run out of ideas or are treading water. Although closely related to the last paragraph, this deserves special mention. Sometimes it's not the ideas or characters or whatever is what's bad, it's the fact that they're using them over and over again. Long running series can have the been there done that feel to them (though at which point people think it jumps the shark can vary - is it because of this villain introduced for the 8th or 9th time that pushes it over the edge to baddom for that person?). Or the plots are near carbon copies of each other. It's hard to tell, except maybe by later interviews, if the team just liked doing the same thing over and over or they actually ran out of ideas, but were forced to create something.
Outside influences. Sometimes the creators have good ideas and would continue to make a great comic, but something outside the team is stopping them. One big example would be the publishers. Sometimes the bigwigs in charge want the comic to change. And who better than people who sit in an office all day would know how to make a good comic? Sometimes it's a censorship issue, and the comic had to be toned down; but if the title was over the top, and it had to be brought a few notches down, it's no longer top-notch, is it? Or they think the comic should go in this direction, or should have this new character, or should be part of this big crossover. Sometimes its due to the comic getting a new publisher, and all the problems with it. Sometimes, a comic isn't selling well, but it's still a good comic. So ways of improving sales are thought up at the board meeting. Changes are coerced ("do this or we're canceling it"), and instead of having a loyal cult of followers reading it, it has no one. Since outside influences don't affect the comic book directly, it can be hard to pin the jumping the shark blame on them, usually there's a lot of suspicion.
Cancellation or termination of series. Though, technically not jumping the shark - for there aren't any bad issues after the last issue - it's considered "bad" for the reader that the series has ended for whatever reason. If used this way (especially if it was canceled), usually people imply that there could have been more good issues if it would have been allowed to continue.
And, if the comic was always bad, people say "it jumped the shark from the beginning." Again, technically not jumping the shark, for when something jumps the shark, it goes from good to bad, but a bad title from its start to its (hopefully soon) finish, goes from bad to good, that is, its cancellation is the best thing that ever happened to it.