Well, I tried chaining for a shiny Luvdisc (since it's so easy to get) but I haven't had any luck. However, I gotta know - will the chain break if I don't beat the Pokemon, or can I just keep running away?
It shouldn't matter if you keep running away. The chain is fishing dependent, not combat dependent. In-general as long as you don't move and never have "Not even a nibble", the chain should stay.
(Although I'm guessing this should be discussed in the other thread...)