Juergen,
Sorry - I read this originally and thought you had solved the problem when you said
"I’ve changed the initialization of the I2C peripheral to get it running. "
Does this mean your problem solved, or is this just something you had already done? Let me know if you need more help - I'll probably have to find somebody more familiar with the bootloader code. Are you using the code documented in SW-TM4C-BOOTLDR-2.1.0.12753.pdf?
Mark