Levi was not discharged early. He served his three years and was mustered out due to term of service expiring.
I woud suspect his age (near 40 in 1864) and the "wear and tear" of service were factors in his decision not to re-enlist. He may also have had some service related disability as he applied for a pension on May 26, 1865 (application #69582/certificate #78208). (A certificate number means he was granted a pension.)
His widow also received a pension (application #233472/certificate #180258). There was no date listed for her pension application.
The application/certificate numbers are important if you decide to order his pension file which you can do through this website.