I had mine for about 6 months without issues. If screen rotation is on in the settings menu, then it should auto rotate unless you have another app telling it not to.
The first thing I would do is make sure you have the lasted version android( settings-about device-software update).
If that didn't fix it, I would then try a factory reset(settings-back up and restore-factory data reset), this will however set the device to when you first turned it on. It will erase any apps or data on the tablet(it'll leave the stuff on your external card alone, if you have one).
You can also install an app like androsensor. It'll at least show you if the accelerometer is working. You can also try a 3rd party app that can control screen rotation.
But honestly, if I were you, I would exchange it out just in case. You should not have had issues out of the box.