The Nexus 7 seems to be quite sensitive to bad cables when charging. It might be that your cable has worn out and isn't carrying the current as well as it should, so it is probably worthwhile trying out different usb cables.
Specifically, the Nexus 7 is sensitive to the voltage it receives and it doesn't charge well when it is too low, a poor quality cable has a higher electrical resistance than a good one, this causes the voltage to drop before it reaches the device which the Nexus 7 doesn't like. As a general rule of thumb, thicker cables are better, although it is the thickness of the copper wires carrying the power that is important, so you can be deceived by excess plastic insulation if you are just looking at the thickness of the cable.
If you have a power meter device that you can plug things into to see how much power they use, this can be a quick and easy way to see how well it is charging with any particular cable, my power meter registered a draw of 7-8 watts for the charger with the original cable, and another good quality cable I had.
Sent from my Nexus 7 using AC Forums mobile app