Sorry to hear that Andy. In general, thin wires solder just fine, too, but there can be other problems. In particular, insufficient or ineffective solder flux, attempting to use lead-free solder (just don't bother with it; it sucks!), too much corrosion still left on the wire or contact that are to be soldered...
Some general advice:
- Ensure the wire and the contact are absolutely clean and free of any corrosion. On old equipment I often resort to scraping the muck off with a scalpel etc., but be careful not to cut the wire.
- Use a soldering iron with temperature control and set it to 280C to 320C. Start on the low end and if that doesn't work, inch up a little higher.
- Use a regular 67/33 Sn/Pb solder with a flux or rosin core. Thickness doesn't matter that much, something like 1mm tends to be convenient.
- Use some additional flux or rosin for good measure, although I find this is usually not necessary in a situation like this if you use a good quality flux-core solder to begin with.
- Wet the wire and the contact with solder separately so that they're nicely covered. If the tin doesn't flow easily after heating up the part and then touching the solder wire to it, go back and clean some more.
- Now touch the wire and the contact together, press the solder iron to it and after a few seconds, touch the contact with the tip of the wire. A bead of solder should now flow into the contact zone. Take away the solder and the soldering iron and leave the contact alone for a few seconds to set.
If you could post some pics of the parts in question, maybe I can give some more hints for your specific case.