Setting RTP to continuous will fix this problem, but can cause excessive data use on a metered service like cell phone data service. Also, as the manual says, it also can be a security issue.
I'm using WSJT-X at the RCC console end and finally got it working properly by NOT using the CAT PTT option. There seems to be an issue with passing audio thru the Mic jack on the control RCC when PTT is not active. I don't want to use RTP set to continuous because the primary use of the RemoteRig setup is for SSB. I opted to use the DTR method of PTT in WSJT-X software for the Kenwood TS480. This requires another serial COM port, but works well. I'm presently using a RigBlaster nomic interface and 2 USB-to-serial adapters on my laptop computer.
During troubleshooting I watched the serial data stream coming from the computer to the control RRC. The WSJT-X software sends the CAT command "TX;" instead of "TX0;" when using CAT PTT. I compared this to Ham Radio Deluxe and the Kenwood ARCP software that uses the "TX0;" command for PTT. At first I thought this was a problem, but the Kenwood documentation says that the command "TX;" will default to "TX0;". (see the attachment)
If you don't want to use 2 COM ports (one for CAT and the other for PTT) you can use the Signalink-USB and eliminate the need for a USB to Serial adapter. But, you will have to use the VOX option within the Signalink to provide PTT. Not always the best choice, but it should work.
73, Joe, K1ike