Lift in a turn has both a vertical and horizontal component. When you pull up in a steep turn you are increasing the horizontal component and the increase of the horizontal component comes at the expense of the vertical so at a certain point vertical lift decreases (descent) as horizontal lift increases (tightening the turn).

In the normal steep turn maneuver, you can compensate for small losses in altitude with early response on the yoke, but even then, the goal of learning and teaching the maneuver includes an understanding that larger excursion require a decrease in the bank angle to recover.

If you're the seeing is believing sort, try this – do a commercial steep turn (might as well get the "advantage" of the extra bank angle). Once in the turn, establish a 100-200 fpm descent and then try to level off using only the yoke (as a CFI candidate, you might try this with your instructor). Do it enough altitude so you can give it enough time to see what happens before you roll out and recover.