Why when someone is doing a beat down...
 

Do they ring the bell constantly? Is it meant to annoy the heel so much that they will stop?

Yes

Wouldn't you keep ringing a bell if you saw someone getting beaten on by a gang?

Probably (kayfabe) to remind them that the match is over and they can stop beating the shit out of each other.

Adds to the heelish-ness 'cause it makes the guy look like a rebel and he dont care about rules.

It is probably a sound like a firebell to alert the random referees and road agents to come down to try to break it up.

This.

The fan that rang the bell during the Nexus debut had the right idea. Without him ringing the bell, maybe nobody would have come out to help Mr. King.

On a bell-related note: Why does TNA ring their bell like, 7 times after a match? I feel like 3 is enough to signal the end.

I'ts better if you just leave that question open ended. It's what's going to happen anyway.

It's the new cutting edge thing. It enables them to believe that they are doing something more than the WWE ever could fathom.

It's also to show how crazy the clusterfucks have become in TNA. So many more bells means it's getting crazy up in the Impact zone! Too bad they don't charge people to enter the Impact Zone. Jim Cornette said they should think of a way to make people pay to leave it.

video?

Jim Cornette is a dumbass.

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Around 3:30 (should start there) after the timekeeper is attacked.