Radio cuts in and out while car is running.

Voltage to the radio is not consistent. Using a multimeter check that both red and yellow wires show at least 12 volts while the car is running and never goes higher than 14.9 volts.
Ensure the ground (black wire) is connected to a clean metal point not shared with other electronics, such as tach or gauges.
If running an electronic tach, be sure the tach input wire is not routed over the radio area.
Some High Energy Ignition (HEI) distributors can create interference. Be sure there is proper shielding on your firewall between the radio and the HEI distributor. In some extreme cases, it may be necessary to relocate the Radio Motor away from the firewall.