As far as Kindles and Kobos go, since they'll rarely (it happened a grand total of once for each vendor so far) update the base system (i.e., glibc), the only thing that might have an impact on us would be kernel updates. They used to be fairly frequent on Kindle (much less so for the latest round of MTK devices, though), and much less so on Kobo (that hasn't been the case for *some* AW boards, though, especially the Sage, which has seen frequent kernel updates).
Said updates *might* have an impact on us (i.e., the AW updates have affected some of the weird sunxi display driver quirks, sometimes in a good way, sometimes in a not so good way
).
PocketBook is another kettle of fish because of the InkView middleware, which adds another layer of random blackbox fun in the middle...
And Android, as @pazos just said, is a wonderful and horrible mess, so, surprise!
TL;DR: My usual advice is:
* Kobo: keep it up to date, it's good practice and very unlikely to cause issues, but might very well fix something that matters.
* Kindle: would have been the same advice, except JB concerns make that a touchy subject ;o).
* PB: meh.
* Android: double-meh.