You gotta know what kills a pun. It's like knowing that drinking anti-freeze kills you. So you don't do it.
The articles in this section are all focused on puns dying.
There are several warning signs for a dying pun: It's being used too much, Buzzfeed stole it and put it on a post, or that it simply isn't funny.
If a person hears a pun too much, it will become annoying. No one wants to hear you say "I can't do this anymore" while holding up a can if you constantly repeat it to everyone you see. If you get to the point where someone says "Oh I've already heard that pun", you need to stop.
But, there are other ways for a pun to die that aren't in your control. For example, if you tweet a pun, and some large mainstream blogging website like Buzzfeed picks it up, there's no hope for it. This also goes with stealing puns from Buzzfeed. If you steal a pun, especially from something as mainstream as Buzzfeed, most people will have heard that pun. This will either evoke a fake laugh and silent judgement or a "Oh yeah I saw that pun too". No one wants that.