I am starting following command from a bash script (arguments omitted for simplicity)

avconv | sox | nc

I am starting about 150 such commands on the same box at the same time.

The last nc command sends the stream to another host. When that host dies, nc dies but avconv and sox can stay alive. I don't know exactly why there is no sigpipe to kill the whole chain. Maybe the system is highly contended and all buffers are full and waiting for some reason? How can I set up this pipe chain so that all processes terminate if any of the 3 processes terminate?

that should be done "automatically", so I would say you do not need to do anything.
From the other hand I think (so it is my own opinion) if you start 150 chains of commands you can be confused about the result.
(just a comment, nc is not trivial, it can be netcat, nedit client or something else, I assumed it was something like netcat)
If you need more help you need to give more information (like what's happened on the other side).

The problem is that it does not happen automatically. I'm not sure no data is being written or there is another issue, but when the target host goes down, I see 0 instances of nc (netcat) and lots and lots of instance of avconv and sox left. They don't die until I do a killall.

My problem is that my re-try mechanism does not work when the target host goes down because only nc terminates, but the other processes don't. Therefore, the parent process stays alive and there is no re-start.

Are those processes actively writing anything to their output pipes? Each process must discover its own broken pipe (the pipes are entirely separate), but a broken pipe is only discovered when a process attempts to write to that pipe.

They should be, but even if they don't, I would like them to close. Is there a way to bind the lifetimes of these processes together so that they exit together without strings attached?

in that case I think you can reproduce that problem easily, you only need to "cut the wire". I do not know how was nc configured, but actually nc should catch the event (something like connection lost) and you can also handle it: