The answer varies depending upon the vendor that is hosting the book.
For example, in EBSCOhost, you can download or check out books for offline reading for up to 168 hours (7 days) or longer, this date varies per publisher restrictions. See instructions for checkout and downloading here. Once the check-out period expires, you will be able to check out the book again if you wish.
Other vendors (for example eBook Central) will typically explain their check-out (or download) options -- if any -- when you click a book's download link.
If you don't see the information that you need, look for a "help" or "support" link (often located along the top of the screen) and search there for information about check out periods or downloading.
Of course, as an alternative to downloading, you can read the book online. Some of our book suppliers, like EBSCO and Ebook Central, allow you to place your favorite books in a folder or bookshelf, so that you can access them easily. Books in your My EBSCOhost folder or Ebook Central bookshelf will remain there for online reading for as long as your account is active.