Recently bought an electro-acoustic, which I love. However there is a strange issue i'm having. To get any sound I must pull the cable out of the output jack slightly on my guitar. I've removed the output jack from the guitar to see the wiring connections and they are all good. The cable itself is snug in the jack, it doesn't fall out or feels lose.

I'm just a little confused on the issue here? Is the jack itself damaged? Or could it be the cable itself, (I've only tried one).
Is the jack stereo or mono? Does it have 1 or 2 rings on the tip?
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Try a different cable. The 1/4 inch jack standard is not a standard at all and variations of socket and plug are not always compatible. If this does not fix then maybe socket of guitar needs a tweak to its inards - may not be switching the battery on.