There are two schools of thought here. Ash is right about not wanting to be tight, gripping too tight, and being overall too tense within the service delivery. This, as most people know, will diminish racquet head speed which, in turn, will limit optimal spin, maximum racquet distance, and overall ball velocity.
On the other hand, as Raul pointed out, those who have a grip-shift habit will shift the grip more when the racquet is held too relaxed. The grip shift occurs as the racquet moves into the collapse phase of the backswing. Thus, it is usually the most unconscious moment of the player's feel of the racquet in many cases. This transition from near collapse to the upward acceleration point in the swing causes many players to re-grip the racquet as the hand tends to want to grasp the racquet in the stronger Eastern Forehand grip, (but, obviously, a weaker overall grip in terms of a skilled serve.)
In training a player to not grip change in mid swing, sometimes doing a hundred serves with a conscious, firm grip within the backswing component, can help a player break this habit. After which, the player can then be more relaxed and work the rhythm of the serve without this tension. But, to break a habit, one must make themself aware of the movement through conscious practice. May take many days of working this drill.
I will have to look and see if I did an article on grip shift for TennisOne...I may have many years ago...or it may have been part of an article on problems on the serve. (Grip shift being one of them.)
If I locate the piece, I'll either post the text here or provide a link.
Dave Smith: Author, Tennis Mastery/Coaching Mastery;
Senior Editor, TennisOne; Dunlop Master Professional