Why do I get no text alert for one contact only? I have an iPhone 5s and when my mom texts it doesn't make a noise. It does when everyone else does.

There is a small gray moon next to her name, but I have checked and her phone is NOT on "Do not disturb". Any suggestions?
Your phone may not be on "Do Not Disturb," but that conversation is - it's a separate setting from your phone's "Do Not Disturb" setting.

Just go into that conversation -> Details -> toggle the Do Not Disturb switch and you should have your notifications back.