Not my belief, but I heard a 3rd-grade student of mine earnestly explaining this to another today and just had to share it: If you are sick on your birthday, then you don't get one year older.
A childhood belief about birthdays

others believed things like this
- My cousic used to think he was older than me because his birthday was in June and mine was in December.— //**...Ethan...**\\
- i thought I got one year older when my family sang the birthday song.— I am the ghost
- My parents have the same birthday -- month, day, and year. I though all mom's and dad's had the same birthday.— Cait
- i used to think that i was older than my dad because my birthday was before his— zara
- My birthday was on a different day every year, assigned by my parentsAnon
- I used to think that your birthday changed every year, and that your parents just decided what day it was.— Daniel