ADC output Unstable
So, does the reading stabilize after a while or does it continue to increase?
My guess would be something in your system is drifting due to self-heating. Check that your input clock and Vref is stable over temperature. After that... most electronic devices have temperature coefficients, so it could be almost anything, including the resistors you are using, that could have a lousy temp coef. The datasheet should tell you what kind of temperature drift you can expect from the ADC. You either have compensate for them, wait while the sytem comes to a stable operating temperature then recalibrate, or put the whole system in a temperature stable oven.
Good luck.