Since Rhapsody has still not fixed the connection timeout problem, I developed an ugly workaround.
Create a batch file with the following contents:
[FONT="Courier New"]@echo off
for /f "delims=, tokens=2" %%x in ('tasklist /fi "imagename eq rhapsody.exe" /fo csv') do set rh-pid=%%x
if %rh-pid%=="0" goto start
netstat -o | find %rh-pid%>nul
if errorlevel 1 goto restart
echo Rhapsody is running, but has no active connections. Killing it...
taskkill /t /im rhapsody.exe
echo Starting Rhapsody
start "" /min "c:\program files\rhapsody\rhapsody.exe"
Create a shortcut to that batch file, and flag it to run minimized.
Use task scheduler to schedule that shortcut to run every 10 minutes.
If I get around to it, I'll rework this as a vbscript so it doesn't pop-up a taskbar entry every 10 minutes, and minimizes the Rhapsody window when it starts.