Mine used to do that. It was a glutton. For some reason it died. I had it for 2 years, which isn't a long life for a Betta. That was before I knew that Bettas need to be kept in 5+ gallon aquariums.
...STARVING.. WHY..? I Feed my Betta everyday, I can't even skip a day due to he acts like he starving, Had her for 2 weeks, I feed her twice a day with Betta pallets, and once a week Blood Dried Worms...for like an Snack.. She goes to the top and constantly searching for food, she digs in the gravel looking for food and when I feed her 4 Pallets twice a day once I place them in the Tank she eat them less than 30 seconds.. and search for more do she suppose to act desperate about food like, this she love her food and she runs to the tank when I come buy the Tank and open it she acts human...Any one else Betta do that...