This is a common problem caused by excessive pressure while playing.  Usually the player will press the mouthpiece progressively harder against their lips as they try to play higher notes.
The root cause is usually an incorrect embouchure with the player stretching their lips by smiling to play higher.  Eventually, the player can’t go any higher because the lips have been stretched their to their physical limit.  The player can temporarily stretch the lips even further by pressing the mouthpiece into the lips.  This process can damage the lips to the point where the player cannot continue to play higher notes at all and will need recovery time.
The solution is to change the embouchure to push in towards the centre of the lips with a pucker instead of stretching outwards with a smile.  The player can essentially develop an unlimited upper register, without applying any pressure, by developing strength in the lip muscles.