Two things come to mind:
1) When the computer reboots, the state of the serial port is undetermined, so you have to accept the key-down or disconnect the repeater or Rigblaster during boot.
2) It sounds as if the idle state of the lines is set to key down, and the program is set to keep them active for key up - which would have the Rigblaster key down when the program stops running. I've never used Echolink with a rig, but I suspect that you can reverse the keying sense in the software and in Rigblaster. A voltmeter would tell you what's going on here. Active is around -10v to -12v for an RS-232 pin. The pins should sit at a slightly positive voltage when the transmitter shouldn't be keyed. (Computers rarely meed RS-232 specs, which call for +12 idle and -12v active. But the Rigblaster should work with -10v active and a couple of volts positive for idle.)