Forcing the player to repeat puzzles that they technically already completed before can become boring for the player, and be seen more as a chore. Utilizing similar mechanics is important to teach the player, but by using the same exact puzzle design for multiple levels or points of progression, the player sees through the lack of creativity of the designers and begins to ask "why are you making me do this?" It is not a good idea to just re-skin puzzle design with different colors in the hope the player won't notice.
Examples[]
The Talos Principle
In The Talos Principle, the designers too often use the same puzzle design between levels and to accomplish repetitive tasks. For example, once the player collects enough puzzle pieces, they can open doors and portals to new locations, but the puzzle design is almost always the same; fit the puzzle pieces into the board until all pieces fit the board perfectly. At first, this design is accepted by the player when they only have to use four or five puzzle pieces on a board, but later on the puzzle design becomes more of a frustration when each board uses eight to twelve puzzle pieces. The issue is not the increase in puzzle pieces, but more so that the exact same puzzle design is re-skinned in just a larger board without any new elements.
Zero Time Dilemma
Zero Escape: Zero Time Dilemma has a few repeating puzzles, of which, a couple of them never really iterate on the original design. One puzzle in particular (similar to the puzzle above), is repeated about four different times in the game, each time just giving it a different skin. This leaves the player bored after completing it a couple of times.