What would cause the time on radio to stay when truck is turned off?

The most likely cause of this issue is a faulty ignition switch. When the ignition switch is turned off, it is supposed to cut power to all of the electrical components in the vehicle, including the radio. If the ignition switch is faulty, it may not be properly cutting power to the radio, which would cause it to stay on even when the truck is turned off.

An alternative cause could be a faulty connection between the radio and the rest of the electrical system in the vehicle. If a wire is loose or damaged, it could be causing the radio to receive power even when the ignition switch is turned off.

Finally, it is also possible that the radio itself is faulty. If the radio's internal circuitry is damaged, it could be causing it to stay on even when it is supposed to be turned off.

If you are experiencing this issue, you should take your vehicle to a qualified mechanic to have it diagnosed and repaired.