Your alternator is most likely only putting out 40-50 amps at the very most, your cars computer, fuel pump and other electrical loads that you have no control over are most likely drawing 10-15 amps and your starter is drawing 200 amps or more for a few seconds every time you use it so it sounds like you need a larger battery and charge it more, a solar trickle charger is going to help your battery up to a full charge and thus keep it lasting years more.
leaving your battery partly charged while parked for hours at a time is going to play a big role in how long your battery will last as it sounds like you never run the engine long enough to recover from using the starter.
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