Based on the information you have provided, it appears the issue is more related to proper battery storage and conditioning than the charging system in your C4. Unless you have the time and equipment, I would suggest replacing the tender (trickle) charger and battery. It would not hurt to take the battery and alternator out for testing at an auto parts store. A bad battery can cause the alternator to over heat, and you should not use the cars charging system to charge a weak or dead battery. Get yourself a DMM (even a $5 one will work) and record the battery voltage at the terminals several times a week. With a good battery a battery tender should have no issue maintaining voltage readings above 12V. If it drops below 12V then something is not right. Mine will maintain 12.4 - 12.8 volts even in the dead of winter. A tender charger will cycle on and off (should have charge indicator lights). Here is a simple test. With a fully charged battery (charge indicator is off), you should see it cycle back on when you turn on the headlights (may take a minute), then off when fully charged. If the charger is always on or always off, this is an important hint something is not right. Cycle times will vary based on ambient temperatures, tender output rating (amps) and the condition of the battery. When you purchase a new battery ask or check for one that has the latest date code. Most auto parts stores rotate stock so you end up with the oldest one.