There's no missing scales, or visible cuts? If there is, he rammed his pretty little head into something and that would be slime coat protecting the body from infection.
If not, it is columnaris. And bettafix is absolutely useless. Tea tree oil coats the labyrinth...
A proper cure, would be any fungal cure that rids columnaris. Jungle Fizz Tabs, API fungal cure, Maracyn (2?), etc.
How often do you clean the 1 gallon?
Is it heated?
If it is not heated, that is a problem. Betta fish are tropical and more prone to diseases when in improper conditions... Like cold water. a 1.5 is easier to heat, 2.5 safer to heat.
1 gallon tanks, really aught to be cleaned every other day, at least. Mainly because the ammonia build up can be so ridiculous... And dangerous. When the immune system goes down from it, BANG! Diseases. And parasites too! Not the greatest thing for your little pet.