Why do accelerometers drift?
The reason is that the test mass inside the accelerometer is subject to gravity.
Do accelerometers drift over time?
The short answer is yes; they do change characteristics with time - and I have measured them to do so.
What causes integration drift?
It is a well-known fact that the use of numerical integration of acceleration/angular rate information from inertial sensors (accelerometers/gyroscopes) to obtain position/orientation information inherently causes position/orientation errors to grow with time, which is commonly known as “integration drift”.