If it’s DOA, please contact customer support for a replacement. (They should definitely not die immediately.)
Generally, though, the pen-lift servo is the one component that you should expect to wear out over time.
The primary limit to the lifetime of the servo motors is that the tiny DC motors inside them wear out. Once a servo starts buzzing, that means that it’s moving its motor constantly, and will die very soon after. (Buzzing means that the motor is moving constantly.) Heat seems to be a factor, so reducing the stroke or the amount of weight to be lifted can help extend the life. Applications where the servo has to move more weight (including rubber bands, weights, etc) tend to reduce life further. If your pen-lift stage doesn’t glide smoothly up and down, then we should address that, as it’s one of the biggest factors that can give you a reduced servo life time.
One other concern is that the motor may still jitter while the machine is not otherwise in use. We made a change in the most recent version of the EBB control board, adding a MOSFET to control servo power. (This version is distinguished by using a micro-USB connector, rather than a mini-USB connector.) This allows you to turn off servo power, and (by default) does so automatically after 15 minutes. From the age of the machine, I’m guessing that you have the mini-USB connector, not the micro-USB connector. Accordingly, it’s a great idea to unplug the AxiDraw from power when it’s not in use.