The radio on my Coby 610 turns off after 3 minutes of play
I don't think I am actually solving this, but I think I may have a reason why it is happening. I am having the same problem with the radio turning off after about three minutes (I, too, had to reinstall the firmware).
I think the system sees the player as "inactive" when in radio mode and shuts down after a few minutes of "inactivity" -- even though you are, in reality, listening to the radio. The exact same thing happens when you pause an MP3 you are listening to; the system will see the player as inactive (because the music is paused) and shut down after a few minutes.
Maybe there isn't anything in the system (firmware?) that can differentiate the inactivity of just listening to music coming in through an antenna and the inactivity of paused digital music?
Feel free to send this to Coby tech support and see what comes back.