Sounds like the lever that holds the shell in the magazine tube is releasing early. Might be crud gumming up the works or just wear on a gun that lasted a hundred plus years. SDH has a good article on Burgess pump gun in the November Shooting Sportsman. Drop him a message about your problem.
You do know I am sure that your new gun is about 120 years old. Well made but not the strongest design. Light use might be fun and you do not have to worry about seeing very many of them at the gun club. Years ago I saw a snob lording over us peons with his D grade 1100 like it was a one of a kind super gun. When a F grade showed up one the same squad he shut up a d soon departed. I learned that day there is rare and then very rare.