It could be shorting through the jack. You can test it by pulling out the jack and checking for connectivity across the two leads which act as the switch, which are ring and switch in the diagram below.
http://www.stewmac.com/freeinfo/i-1521/i-1521.pdf
Also, check that the connectors haven’t bent and shorted through the screw-on metal shielding cap (if it’s installed). I’ve found that condition on a couple of guitars and it’s led me to use heat-shrink tubing on each separate connector on any Switchjack I install, because it isolates the switching connectors from each other and from the cap.
-mh