Most battery chargers are trickle type chargers - that is, they provide a constant low current (under an amp) output at 12 - 15 volts to keep the battery charge up. This small charging current is handled easily by a #14 or #12 wire which will pass up to 2 or 16 amps consistently, respectively (the larger cables off the battery are for the starter motor).
If you're having trouble maintaining a charge on the battery, a careful check of the charging circuit is required. Look for loose or corroded connections - at the battery in particular, open or blown fuses on the input (120 volt) side of the charger and the 12 volt output side (if provided). Battery acid is conductive. This means if there is a path of battery acid from one post to the other - no matter how long or short the path - the battery will discharge through this path. Neutralize (with baking soda) and clean any battery acid from the area to be sure the battery isn't discharging faster than the trickle charger can charge it. You can check the output of the charger with a DC voltmeter. Simply press the test leads to the battery posts and some value above 11.5 volts (11 - 12.75 volts may not be uncommon). Look at the chart below to get an idea of the charge of a lead acid battery
With the battery disconnect from the charger (or the charger powered off), the meter should show indicate 12 volts (even if practically dead) without a load. That's why it is important to load the battery when trying to get a voltage reading from it. Many auto parts stores sell and loan battery load / meters expressly for this purpose. They look like this:
If you have a battery that won't stand up under load, you may have a a problem with acid / distilled water level or even a dead cell. You can not check these variables in a maintenance free battery however. If you have removable caps on the battery, check and top off the level with distilled water only to a "full" or "high" level mark. A hydrometer can be used to determine the charge of each cell in the battery. These can be had for under $10 in most auto parts stores, too. They look like this:
Make sure you get one to check the specific gravity of battery acid - NOT to check anti-freeze level protection - they look similar.