The most likely answer to this question is that your Internet Service Provider (ISP) may be blocking those emails by what is known as a spam blocker. In case the term "spam" is alien to you in this context, here is the definition: Spam is basically junk email. A spam "blocker" or "filter" looks for certain words or phrases that spam traditionally uses, such as "sale" or "advertise". The filter then takes these message and deletes them or adds them to some sort of bulk mail folder. What you need to do is go to that bulk mail folder and "white list" your library's email once you find it. When you white list the address you are telling your spam filter to accept emails from that address as legitimate. If you are unable to find an email to white list, you can try entering the address in manually. Most library patrons receive email notices from firstname.lastname@example.org. Once you white list that address you should be okay.
Invalid email address
Another potential problem is that your library does not have a correct email address for you. If you think this could be the problem, please contact your local library and verify that your email address is correct.