Unless you wear a hat at all times for cultural and religious reasons, this is not likely to be causing your hair loss. Infrequent wearing of hats or helmets does not cause any harm. If you wear the same hat all the time, be sure to use good hygiene in washing your hair and keeping the hat clean. Don’t wear a hat that fits too tightly. If you’re getting suspicious of your hat, it’s prime time to get a hair and scalp assessment.