is the resistance in ten meters of copper wire too high to use in a circuit powered by AA batteries?
24 AWG wire is 30.2 milliohms per foot.  

10 meters is 32.8 feet

so 10 meters of 24 AWG wire is 990 milliohms.  But you actually have twice that, because the current goes from the battery and back.

So 2 ohms for wire resistance.

AA batteries have a series resistance of about 0.5 ohms new, and more as they age, so the circuit is probably happy with a little series resistance.

If the wireless transmitter draws a peak of 100 mA (a guess) the voltage will dip an extra 0.2 V because of the wiring resistance.

I think it would work better with 18 AWG wire, which has about 1/4th the resistance of 24 AWG.