I keep my router and computer on a battery backup. However, if the battery is bad in the ONT (box in your garage), power flickers in the FiOS system will still cause temporary outages.) Depending on the model of yours, you can find them on Amazon.com cheap. I bought this replacement for mine.
http://www.amazon.com/gp/product/B0010Z4MDK/ref=oh_details_o00_s00_i00?ie=UTF8&psc=1
$12.99 with free shipping and easy to replace.