Is the "S" showing in the display just to the right of the frequency when this happens? That would mean lock out on high SWR. If that's happening, check your dummy load or the coax or adaptor you are using to connect it to the QMX.?
In the meantime, you should probably be using the Practice mode found in the CWKeyer menu. This allows you to practice without generating any RF.
I have been using the QRPLabs dummy load connected to my QMX, with a Begali paddle, to practice my morse sending. The issue I have is a little random in that the length of time that things are ok varies. After perhaps 1 to 2 minutes of sending with decoded letter appearing correctly on the screen the QMX will just lock up - i.e. no further tones heard or characters displayed. I have to turn off the power then turn on again to continue 'sending' morse. Please let me know if a short video demo would help make theissue clear.