You can’t (and shouldn’t) keep a library book forever, but if you’re not quite done with a book, then you can do the following to finish it:
Do not close the ebook to look at another book or adjust a setting. Rather than powering off your Nook, only let it sleep. Do not hook the Nook up to the computer or otherwise charge it.
According to other Nook owners, this will keep the book from expiring. Of course, you’ll eventually have to charge it, but if you’re lucky you should be able to get it done before you’re done reading. A better idea is to always check out your Nook ebooks for 21 days, since you can return it if you finish early.
eRead Me Vegas - FAQs, Tips & Tricks 
Thanks, I thought I had requested 21 days, but only got 7, need that little extra to finish it.
Try setting your date back on your reader the number of days you need. This will fool the reader and ebook to give you the extra time.
To set the date back, look for a setting on the ereader. You should find a date/time setting there.
Did some more research and found the Nook with 3G gets the time from the ATT Cell phone tower. It appears to be a problem with a lot of people as the device is made in China and needs to synch with the 3G tower in order to get the correct date and time. It is recommended you request B&N to provide a manual setting for date and time in their next firmware update.
What does this mean for getting extra time to read the book? All I can suggest is either check it back out and download again if you can or if their is a waiting list, sign up for the it again. Unfortunately there is nothing else we can do.
Another suggestion: You might try printing the pages you need from the computer the ebook was downloaded to. Many of the books allow a certain number of pages to be printed within a time period. You will have to check what is allowed in the eMedia Catalog on the main record page for the book.