Do breast implants sag quicker if they're placed over the muscle?

Yes. When implants are placed under the muscle, the muscle provides some support and thus reduces the tension on the breasts.

Implant sagging is less a function of implants but rather soft tissue/skin quality. That being said, I do believe a submuscular implant does benefit from greater relative support in the lower pole.

Aesthetically, implants placed superficial to the pectoralis major create a rounded, convex appearing breast profile. This effect is camouflaged, at least initially in larger breasted patients. However, as a woman ages fat atrophies and breast tissue descends. The result is a more noticeable implant specifically in the upper pole. Similarly, patients who have thin coverage superiorly are more likely to be able to perceive the implants and at higher risk of visible rippling.

As always, discuss your concerns with a board certified plastic surgeon (ABPS).

Breast implants probably sag similarly whether over or under the muscle. The muscle does not really hold them up. Sagging is often caused by skin quality and other factors. If a patient is going to have sagging breasts, often the implants stay in a good position and the breast tissue sags off of them.