What could be the reason that my four L-16 batteries use a gallon of water every few weeks?

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Overcharging is a likely cause. I would use an accurate voltmeter to measure the charging voltage, particularly once they are fully charged. At that point, they should be charging at no more than the "float voltage" value.

If the batteries are in an environment other than 20 deg C, then the voltages need to be adjusted for the new temperature. The solar controller may have a temperature sensor and provided adjusted voltages. But if the controller is in one location (say in the sun) and the batteries are in another location, and if the temperature probe is located inside the solar controller rather than being located at the batteries, then the solar controller might be putting out the wrong voltage since it is in a different temperature environment from the batteries.

With a voltmeter and a thermometer (to measure air temperature near the batteries), you can test to see if the batteries are receiving the proper charging voltages. Here are data sheets for your batteries. The third one explains how to charge the battery, which might be how the solar controller would do it once the sun comes up:
http://www.affordable-solar.com/admin/product_doc/Doc_8L16-DEKA%20Data%20Sheet_20090517212621.pdf
http://www.affordable-solar.com/admin/product_doc/Doc_Photovoltaic%20Battery%20Charging%20Parameters_20080319154916.pdf
http://www.affordable-solar.com/admin/product_doc/Doc_Flooded%20Charging1_20091028104431.pdf

Here's the manual for your solar controller:
http://www.blueskyenergyinc.com/uploads/pdf/Manual_BSE_SB50.pdf

I see that it provides a float voltage of 13.3V or 26.6V (for a 12V or 24V system). The front panel indicates when it is in float mode. That's when you should measure the battery voltage and compare to the float voltage specification. Similarly, during the acceptance charge phase, you can measure for the voltage of 14.3V or 28.6V @ 80°F.

There is an option for a SensorLug battery temperature sensor in order to provide optional temperature compensation. If you don't have the SensorLug, you should consider obtaining it.

Other factors that might cause problems (see pages 11, 12 and 13):

1. Your system amp-hour rating is 350 amp-hours if a 24V system, and 700 amp-hours if a 12V system. The Float Transition Current Setpoint must be set based on the correct system rating.

2. If you have a constant load while charging, and you are using the internal current sensor, then the Float Transition Current Setpoint must be adjusted further to account for the constant load. Otherwise, the system won't switch to float charging as soon as it should.

3. If you have a variable load while charging, and you are using the internal current sensor, then the setting of the Float Transition Current Setpoint can't be done well. The system would switch much more accurately if the Optional External Battery Current Shunt is installed.

4. Page 13 discusses how to adjust the acceptance charge voltage and the float charge voltage. You can use the procedure to confirm that the potentiometers are not set wildly off from normal....Show more

You did not say which brand of batteries you were using, but:

Charging batteries always splits water into Hydrogen and Oxygen, which gasses off from the cells. Some brands make their plates stronger by adding Antimony to the Lead, which increases this effect, but can make the battery last considerably longer ... as long as you watch the water level.
Concorde and Lifeline have a newer style of battery called AGM Absorbed Glass Mat batteries that recombine the oxygen and hydrogen so they are nearly maintenance free. Perhaps that will be your next style after the end of life of your present batteries!...Show more