Fluorescent light requires twist to start
The tombstones are defective and this is why you need to twist the bulb. 

The tombstones are the bulb connector mounting - I am guessing you have a Bi-Pin although single pins can have the issue they are less susceptible .

You can replace the tombstones, however the price you will pay for the replacement parts and the time to replace them might not make it feasible. 

I have had this situation and just replaced the unit with a $24 LED unit.