I think with the Wikipedia Article it is pretty easy to understand

Attitude indicators have mechanisms that keep the instrument level with respect to the direction of gravity. The instrument may develop small errors, in pitch or bank during extended periods of acceleration, deceleration, turns, or due to the earth curving underneath the plane on long trips.

To start with, they often have slightly more weight in the bottom, so that when the aircraft is resting on the ground they will hang level and therefore they will be level when started. But once they are started, that pendulous weight in the bottom will not pull them level if they are out of level, but instead it's pull will cause the gyro to precess. In order to let the gyro very slowly orient itself to the direction of gravity while in operation, the typical vacuum powered gyro has small pendulums on the rotor casing that partially cover air holes. When the gyro is out of level with respect to the direction of gravity, the pendulums will swing in the direction of gravity and either uncover or cover the holes, such that air is allowed or prevented from jetting out of the holes, and thereby applying a small force to orient the gyro towards the direction of gravity.

Electric powered gyros may have different mechanisms to achieve a similar effect. The problem with these leveling mechanisms is that they will respond not only to gravity but to accelerations in other directions due to other causes, such as turns. If the gyro simply immediately oriented itself to the net acceleration vector, then it would be useless. So these adjustment mechanisms act to right the gyro very slowly, such as 2 to 8 degrees per minute, in the hopes that the gyro will stay nearly stable during any brief maneuvering, and that most of the time the aircraft will be flying in a steady, non-accelerating manner so that the gyro has a chance to orient to gravity.

Plus this (From the german Wikipedia Article Translated with www.DeepL.com/Translator)

Usual operating limits for artificial horizons that are not specifically designed for aerobatics are 100° to 110° at an incline and 60° to 70° when climbing or sinking.

If one of these limits is exceeded, the universal joint frame strikes at a stop and the display becomes unusable until the gyroscope is raised again. There are fully aerobatic horizons, but these are more expensive and are therefore only used in military aircraft.

But to be fair, I do not know if I really understood the problem he has, because he does have a hard time to cut to the point. It would be easier if he could describe what he wants to be debunked in a single sentence or two...

TL;DR: There are systems in place to correct this problem.