Christoph,
Welcome to the TI E2E forum. I hope you will find many good answers here and in the TI.com documents and in the TI Wiki Pages. Be sure to search those for helpful information and to browse for the questions others may have asked on similar topics.
When the FIFO runs out of transmit data, it will no longer send data to the transmitter and the transmitter will then report a underrun condition. Try this by stopping the DMA channel that is supposed to be servicing the transmitters and check XSTAT to see if the underrun status is set.
Regards,
RandyP