Even if it's leaking, if the gauge is accurate the beer will be picking up CO2. The beer doesn't "know" if the 13psi comes from a single dose of gas or if it's leaking out and more gas is flowing in to take its place. Just that there's 13 psi.
Assuming you have it at a reasonable temp, I'm guessing the gauge is off. One thing I have often found with my gauges is that when I turn them down they are off by several psi. To fix it, I turn it down until the gauge reads below my desired set point, then turn it back up until the needle gets to the right point. Alternatively you can vent the keg and watch where the needle returns to. It's worth checking.
You can also check the gauge if you know someone who has their own setup. Just take the keg to them and have them pressurize to 13 psi, if gas flows in then your gauge is off.
Oh, and just as a sanity check - the gas is really connected? And all shutoff valves leading to the keg are open? I've pressurized kegs and then turned off or taken off the gas for one reason or another, then forgotten to put it back on.