When looking at a set of physical exercises, yes it is possible for there to be plateaus. If one chooses a practice that fatigues rather than energizes it is possible a) that person needs a different practice, b) that person needs to learn from this practice (though it may still be inappropriate for them), or c) that person needs a restorative practice periodically.
However, a plateau (when looking at a physical exercise system, which Yoga is not) typically doesn’t result in “stiffer and weaker”. Stiffer and weaker usually indicates something else. That could be a shift in diet, sleep patterns, seasons, or the overall effectiveness for said practice for said person (as outlined above).
When looking at the bigger picture, Yoga is an awareness practice, something experiential, something that moves the person toward themselves (though some practices unfortunately lead the student away from themselves). As such it is just as acceptable to progress as it is to not progress as long as each is duly noted, observed, and integrated into the human consciousness. This too shall pass, as will whatever is next 
gordon