What is battery or system voltage when this symptom occurs?
Most radios will begin to cut-out at 10.0 VDC while ignition will continue to work (light loads) down to 8.5. Get a volt merter (or similar LED indicating device) connected to the cig lighter.
The wiring, regulator and alternator are all parts of the charging system. Have you replaced the alt with a known good unit?
On a larger note: Even if the alternator and charging system is working properly the [stock] alt is only gonna output 60A with engine >3000 RPM. Depending on the electrical loads, that might not be enough to keep up. Some numbers:
Ignition on, engine running - 8 A
Fuel pump at full chat - 15 A
Running lights - 12-15A
Head lights ( (assuming stock-ish 60W each) - 12A
AC - 12-20A (with fan)
Fog lights - 12A
Turn signals - 10A
You can easily see that running all of the above can quickly exceed 60A. No to mention conditions where the engine is idling.