Cabling ideas for a moving sensor
Use an FFC cable.



Arrange it in a spiral, with your accelerometer in the centre. As ThePhoton mentioned, you must use strain relief at each end of the cable, otherwise you're liable to get fatiguing there.



Alternatively, use a longer FFC, and arrange it like this if you want lots more rotation:



YouTube video of revolving cable chain.

This application uses cable chain, which is better, and can take whatever cables you want. It's more expensive, but still affordable. 2.4ft of chain is less than 20 GBP from RS. You can arrange the chain in the spiral form as I have shown in my purple rendering.



If you're really strapped for cash, you may be able to get away with simply wrapping your cable around the axle a couple of times in a helix. This spreads out the bending motion of the cable along the spiral length, so that no one part of the cable is bending much. We do this in our robots where there's absolutely no room for any solutions involving cable chains. And, while those robots don't usually do 250,000 cycles, we have never seen a cable fail in this situation.