Why do you have so many amps compared to the amount of speakers you have? Are 3 of them 2 channel and one a 4 channel?
Anyway, at idle your alternator is not putting out enough amperage to charge the batteries faster than those 4 amps are draining them.
You also might be running the head unit off the dash wiring which when the voltage gets low will cause the head unit to momentarily shut off killing the power to the amps.
What batteries are you running? and how long do they last at your normal listening levels?
Where does the power lead to the head unit come from?
What size is the HU power wire?