Hi Janos,
Of course re-installing the OS or a new PC is something I will not suggest :-)
I have had seen problems with CCS earlier and re-installing made it go away as have on some E2E threads.
I have run free wire cable between boards of over 6" w/o problems, but then never used it for a long debug which is your case. Connecting Reset may be a good idea but then the DK board does not give out a Reset to the main Tiva either. If you can use the main Processor for further debug and not see any issue then it can be probable that there is some cross talk between the wires for the other 4 lines.
Another thing could be coil a GND wire around the JTAG debug lines, or if possible use shielded wires.
Regards
Amit