The 10.5ah should be plenty and would not expect a large voltage drop from that unit. that said I would expect some sort of volt drop after even an hour of use, at least a tenth of a volt.
Are you getting exactly 13 volt every time you test?
I have not seen the elite 4 dsi. does it have two plugs one power, one transducer?
if you can replace the power supply, or at least strip back some of the wire and see how deep the electrolysis went. ill bet the whole wire is f'ed up.
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