John's advice is good. It's the method I use.
The only downside is that when the break occurs,
some fences will have different ends, e.g. a solid post at one end, and bare wires at the other. When the break is made with this type, the bare wires at one end can overlap and stick out through the fence post of the next bit of fence. However, you can always tidy this up by slightly dragging one end into a better position, using the shift key to prevent a re-connnect.
Cheers
Casper