Foodstick makes an important point. Not all wire is created equal. Copper, as used in electrical wiring, presents a real dilemma. Yes, it's an excellent conductor. Yes, it solders readily. Yes, it's fairly corrosion resistant. Yes, the cost is nominal. But does it resist fatigue well ? No, as a matter of fact it's quite poor in fatigue.
So, why do they use copper when the fatigue life is poor ? Because all the other properties are superb and most applications don't involve much flexing. Plus, designers have found ways around the fatigue problem. The "way around" is to make wire with many small strands rather than just a few large strands. The many-strand wire flexes easily and the individual strands don't see as much stress as a wire with few strands.
The new wire that you use needs to be of a type that is designed for applications where flexing is a concern. Rather than using the first wire that comes to hand, I'd suggest that you do some internet research and find wire that is designed for long fatigue life. I just did a quicky google search and the first candidate source looked pretty good, although I don't know the price or what their minimum order would be.
http://www.daburn.com/2671UltraFlexi...E15681692.aspx
One last thing: Don't make the mistake of thinking that bigger wire would last longer. Yes, a bigger would be stronger for a single pull. But the flex life of a bigger wire over a given radius is not as good. Try to use the same size wire as you found in your transmitter. somebody else in this discussion might be able to look at the wire and tell you what size it is. I'm no good at that, but think it is in the 26 or 28 gage range.
Dick