If you have a separate starting battery and deep cycle battery for bowmount and or downriggers, it might be best to connect the fishfinder to the deep cycle battery.
What is happening is the voltage "at" the fishfinder is dropping below the threshold required to run it. There are several possible things that can be causing the problem. It can also be a combination of causes.

1) Weak battery. If it is not at full charge, or not able to hold a full charge due to age and/or internal fault, when you start the motor it will draw the voltage lower while starting.

2) Too many things running off the same battery while the motor is not running and/or the motor charging system may not have enough charging power to bring the battery to full charge during the time it is running.
3) If charging system of motor is not charging the battery when it is running.

4) Drop in voltage between the battery and the fish finder. This can be caused by poor (or corroded) connections between the battery and the fish finder. It can be fuse connections, battery connections, crimp connections of wires to terminals, switches and/or connectors. Inadequate wire size, possibly in combinations with length of wire and what other accessories are connected to the same wire.

I would check it out in the following order.
1) Make sure the battery is fully charged and the water level in all of the cells is full. If not, top off with distilled water. Then check the condition of all the cells with a hydrometer. They are inexpensive at an auto parts store. Moderate to poor indication on any of the cells indicates the battery should be replaced.

2) Measure the voltage on the battery with everything off and engine not running (it should be about12.5 to 13 volts). Then measure it with the motor running. It should be a volt or two higher, which will indicate that the motor charging system is working.

3) If no problems are found from 1 and 2 above, check and clean all connections between battery and fishfinder. Make sure all connections are tight. Clean metal surfaces with scotch brite pad, emery cloth, or sand paper. This includes fuse contacts. Shiny metal is clean. You can use contact cleaner or WD 40 for connectors you cannot manually clean. Any connectors that are questionable, should be replaced. When installing new connectors to wires, make sure the wire is not oxidized or dull looking.

Hope this give you a start point for checking…