What are possible causes of ESC system shutting off while driving?

There are a number of causes of this. Most common one is a wheel speed sensor issue. The cruise is deactivated if there are any codes or system failures that would be related to the drive train and the traction control system is one of them.

This would cause the vehicle to think it is slipping and turn the light on. However, we would normally have some codes to go along with this light that tell us which direction to go.

Here are a couple guides that will help with this:

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

This guide talks about the ABS light but it is similar to the traction control system enough that it has useful info.

https://www.2carpros.com/articles/abs-warning-light-on-easy-repair-guide

If this proves out to be a wheel speed sensor then we need to replace them but can perform the following testing to confirm it is the sensor itself.

https://www.2carpros.com/articles/abs-wheel-speed-sensor-test

However, I would highly suggest getting the codes before we do anything else.