I managed to break the antenna off my Turnigy 9x Rx in a crash. The grey lead was cut about halfway down, disconnecting the big red heat shrink wrapped thing.
In doing this, have I severely reduced the range of my radio?
The wire looks like it's a very small coaxial cable. How do I go about fixing this? It doesn't look trivial to solder.
Yes, it would greatly reduce your range as the exposed part of the antenna is under the red shrink wrap.
It is a very small coaxial cable that has the outer shield removed for a quarter wavelength I believe. You just cut off the red shrink wrap and accurately measure the length of the exposed center wire, then see if you have enough grey coax left that you can strip an equal amount of the shielding from the remaining part.
If you don't have enough wire remaining. Just open up the case and solder a quarter wavelength piece of regular wire in place of the coax.
Alternatively, you could just buy another one for $9US. If they are out of stock, I'd sell you one of my spares, but your in Australia, so it would probably take just as long...