Batch has covered it pretty well. Your non-replaceable E-Book reader battery may actually be replaceable, but it may be soldered into the circuit board. What make/model is it?
For an Iphone, depending on how much you use it, I wouldn't expect much more than a year. Laptop batteries you can generally hold up better over time because they're not used daily like your Iphone, and the cylindrical li-ion cells generally hold up better the prismatic ones you find in cellphones and smaller electronics.
I really have a grudge against Apple products because a lot of what they design is not serviceable and if it is, it's tough. The Iphone, Ipods, upgrading computer parts, etc. Especially on something like an Iphone where pretty much every other phone or smartphone on the planet has an easily accessible battery. It's really a crime as their aesthetics are more important than serviceability in hopes of you rather sending it into them for repair or wanting you to just buy a new phone/ipod/computer.