ePub (the broad standard used by Google Books, the iBook Store, etc.) and .mobi (used by Kindle and some others) are both HTML and CSS under the hood, with all the strengths and frailties that implies. Worse, the current standards (ePub 2 and the current Kindle) are based on a subset of late-90s HTML and CSS. You can take a look at what's inside an ePub by changing the file extension to .zip and opening it in Finder or Explorer.
HTML is designed to wrap to fit the available viewport, to be resized and reflowed according to user preference settings. These are inherent in the format. Print designers migrating to the web long reconciled themselves to the fact that items on a web page do not necessarily stay where the designer put them. Poets, I guess, are now having the same realization.
There are several conundrums. You can't have a long line of text that runs off the edge of its container, any more than you could run text off the edge of a page. If the container is zoomed out far enough to fit on a mobile device screen, the text may become too small to read. You can't stop the reader (i.e., the user) from changing the text size, and text will inevitably reflow. To complicate things further, different devices have different default and available fonts.
The solution, such as it is, is to create png (not jpeg, which doesn't do well with sharp contrasty edges) images and use those instead of live text, being careful to format to the target resolution as much as possible. Adobe's Digital Publishing Suite does exactly this for digital magazines. All of the "text" you read in "Wired" mag on a tablet is actually part of an image. You gain integrity of layout at the expense of searchability. As a designer, you also have to design every page twice for each target device: a horizontal version and a vertical one, 4:3 for iPad and 16:9 for most Android tablets.
It's worth noting that Steven Drennon's indenting tip is the traditional way of continuing lines that are too wide for a page in print and calligraphy, so this is hardly a new problem. (The traditional ballad stanza was originally a heptameter couplet. The 4+3, four line stanza we use today came much later, for convenience of formatting.)