I stumbled here trying to find how long an e-Ready is supposed to last.
I have a Kindle WiFi. I haven't used it much. I then left it in its box for maybe a year or two, and now it's simply impossible to use. I have to refresh 5 to 10 times to start being able to read. So maybe by just not using your e-Reader or e-Screen for too long (drained battery or not connected), it can damage it.
Some interesting link
https://e-ink-reader.ru/eink_degradation_en.php