I am not aware of any process by which the servo can become unresponsive as a result of the program that you are running. If XY are responsive, then the Z should be responsive as well.
Here are a few things to consider:
* If the motor still moves but the the vertical slide is sticky, that can sometimes result in the pen not falling when it is supposed to. (It cannot explain the pen raising on its own, though.) Make sure that you’re not overtightening the thumbscrew, and check that the vertical slide falls freely.
* If the servo were to lose its physical connection to the control board, it could easily result in this behavior. Carefully check that the servo connector cable on the left side of the base is fully and securely in place. If you have swapped out a servo on your own, check also that the connection of the servo to its extension cable is secure and that the connection point is held securely in place with the cable ties. You might also try wiggling the cable in different places to see if something seems loose or intermittent.
* If you are plotting something with thousands of very short paths, that can be stressful on the pen-lift servo. One of the failure modes of servo motors is that they can become unresponsive when overheated. If you see this kind of thing again, feel the servo motor, to see if it’s overheating. If you do have plots like this, you can help to reduce the stress on the motor (and increase the speed of your plot) by reducing the total pen-up/pen-down travel distance to only as much as is needed.
* If you are plotting something with no pen-lift movement, but instead very long periods of constant pen-height movement (which sounds like it may be the case), one possible concern is that in recent versions of the EBB, the firmware turns off power to the servo after some period of inactivity. These recent versions are distinguished by having a “micro-B” usb connector rather than a “mini-B” usb connector. This normally happens invisibly, without effect. I have not observed nor heard of any cases where the servo raised position as it was powered down, but that is not outside the realm of possibility. If your EBB firmware is v 2.6.0-2.6.2, then the default timeout is 15 minutes. Any Z movement command would reset the timer, and power would not be restored until another Z command was issued. So, if you are doing individual pen-down paths much longer than 15 minutes, please say so, and I can help you modify the software to alter this timeout.