I think I just cured the same problem by doing Remove All breakpoints.
I haven't had a chance to reproduce the issue and test this fix, but I had already tried fiddling with the USB connection and P&E USB Multilink / OSBDM/OSJTAG setup in the debug configuration, restarting Kinetis Design Studio, restarting the PC, etc.
I have had gdb (arm-none-eabi-gdb.exe) keep running in the background sometimes (if this happens, perhaps try using the red square "Terminate" button on the console window), but that is not what was causing this disconnect-after-download issue. It makes sense to me that a badly-placed breakpoint could upset the CPU following reset. Hopefully some other users can shed more light on this?