Leopold Auer (1845-1930), a famous conservatory violin teacher was asked, “How long should the advanced pupil practice?” Here is his answer:
“The right kind of practice is not a matter of hours. Practice should represent the utmost concentration of brain. It is better to play with concentration for two hours than to practice eight without. I should say that four hours would be a good maximum practice time… and that during each minute of the time the brain be as active as the fingers.” (From Violin Mastery, Interviews with Heifetz, Auer, Kreisler and others, Edited by Frederick H. Martens, pg. 11)
A popular saying is “never play faster than you can think”, and along the same lines the following saying which I’ve not heard holds true, Practice as long as you can still think and to just before your physical body tires.
For new or beginning players, sometimes fifteen minutes is as long as we can go. During 1/2 hour lessons, a break is often necessary to re-command the brain and relax the body. At first, the primary technique is simply learning to hold the instrument and bow for required for technique far beyond the requirements of our the current level of technique required to simply play a Twinkle or Go Tell Aunt Rhody. Practice with an intention in mind such as to divide the bow evenly or hold the instrument with ease and with a relaxed left hand, with posture that allows playing with ease without touching the body of the instrument with the wrist. When the mind is no longer able to practice the exercise or piece with that intention in mind, it may be time to stop practice or rest.