What you are experiencing is very common with the more sofisticated sonar units. They use more amps..
Typically a boat wiring harness is made up of minimum size conductors and with all the splices/connections involved with a fuse panel supplied by a larger wire with a circuit breaker, the total load on the fuse panel is inadequate for the additional load of those units. It's not about volts, it is the loaded volts (amps) that the accessories use.
Add to that, aging of the wiring and exposure to moisture and you get even more resistance to reduce the capacity of the accessory circuit.
What Humminbird recommends for their units is connecting the unit power cord directly to the battery and a 3A fuse at the battery. If the cord is to short, extend that with at least 16 guage wire by splicing, soldering, and waterproofing the connection. Remember the fuse size is to protect the smallest conductor of the circuit. A larger wire is even better to reduce the voltage loss due to the resistance of wire length.
I used 12 guage marine grade wire to extend my power cords.
Another issue that some don't think of is the health of the battery that is connected to the accesories and they depend on the outboard motor to keep it fully charged. Unless you make long runs, you don't replace the loss charge from using your electronics/ pumps or even from starting the engine.
What you are requiring of your starting battery is a quick, powerful discharge to start the engine and then you want it to function like a deep cycle battery to power stuff when the engine is not running.
If your battery is in good condition with clean and tight connections and the units shut down when you start the engine, that means the battery does not have the capacity to handle all the stuff at the same time and/or you wiring is inadequate to handle the load.
Your battery size should accommodate the MCA your motor requires plus enough reserve capacity to handle the deep cycle use between charging cycles and additionally use a charger on that battery when off the water just like you would your trolling motor battery/s