We've never had this occur in the last three years.
Wouldn't there need to be a voltage drain somewhere for the battery to discharge without anything drawing current?
No, not a voltage drain, a current drain. Current is flowing charge, so it means the current drain is discharging the battery. This old EE says the following:
1) I agree with the others - you need to dig out your VOM, set it to measure voltage, and see what (a) the voltage is at your battery when the alarm goes off, and (b) what the voltage is at alarm when it goes off. There are a number of likely possibilities (and a grunch of less likely possibilities). I'll talk about how to find the likely ones. You are likely to find one of these possibilities:
a. Your battery is actually well charged, voltage at the battery is OK, and you get the same voltage at your alarm. The alarm is not going off a the right voltage -- adjust or replace the alarm.
b. Voltage at the battery is OK but voltage at the alarm is different and lower. Look for poor connections from the battery to the alarm, or bad or inadequate wiring.
c. Voltage at the battery is actually low, and you read the same voltage at your alarm. It could be bad wiring, or it could be a bad battery. You need to perform one more test to tell which it is. So ...
Set your VOM to measure current instead of voltage, range up to 5 amps. Turn everything off as you had it before when the alarm went off. Remove the hot lead (+) from the battery and connect it to the black lead of your VOM. Attach the red lead of your VOM to the hot lead of your battery. Read the current flow. If it reads zero, keep switching the range down until you read microamps (which probably isn't accurate, so if it is zero or a few microamps, consider it to be zero).
c.1 -- if the current reads zero or nearly so, then you have a bad battery. Replace it. Have a battery place test it first, if you like.
c.2 -- if you read non zero current, then you have a high resistance ground. That could be a bad semiconductor in some electronic gear, it could be a corroded wire where the insulation has also failed and it touches a ground. It could be a poor connection to something, It could be a bad circuit breaker or switch, It could be anything wired directly to the battery, such as your bilge pump. It could be something you left on or plugged in inadvertently.
If c.2 is your answer, you will have to do some fault isolation. Start unplugging stuff one thing at a time until the current drops to zero or nearly so. If that doesn't work for you, start disconnecting circuits one at a time from your battery or the power distribution panel until the current drops.
Personally, I'd start with the bilge pump, especially if it has an electronic water level sensor. Both the pump and the wiring sit in grungy water, an environment that is fairly hostile to electronics.