Hello,
even if you compensated the tilt error mentiond by Neil with the integrated offset calibration, the offset-accuracy is still limited to ~7mg (as the resolution of the offset registers is 15,6mg). 7mg integrated over 30s already give you a velocity of 2m/s. Is your observed velocity drift in that range? Then you can't get it much better than that. All remaining errors and drifts come on top of that.
The usage of acceleration sensors alone for velocity-tracking and position-tracking over long timescales is quite limited.