I know it might seem awkward, but I would contact the mom. This happened to me with my daughter's party when one of her friends from school didn't receive the invitation because of a typo that I made in the address. In hindsight, I should have contacted the mom to confirm with them when they didn't RSVP, but I didn't want to seem pushy. It wasn't until several weeks after the party when the post office finally returned the invitation due to the incorrect house number that I realized what had happened. I immediately called the mom to apologize, and she was grateful to hear from me. She felt awkward, too, about calling me when she never received an invitation after receiving the "save the date" email. If one of us had gotten passed our awkwardness, the little girl could have attended the party, and my daughter wouldn't have been disappointed.
BTW - those of you who were judgemental about sending a "save the date" in the first place should reserve your comments. There are plenty of legitimate reasons to send one, such as summer birthdays and family vacations, as one other mom mentioned. I sent mine because there was a snafu in printing the invitations that caused a huge delay which was outside of my control, and I didn't want my daughters friends to make other plans and then have my daughter upset because no one was able to attend her party.