Ex-battery distributor here, the previous posters have already mentioned items that must be checked, but allow me to summarize:
* Is there a drain on the batteries? This can be checked by placing an amp meter in the circuit. You will need a meter that will read at least 10 amps (a cheapie Harbor Freight multimeter will do for this). A battery cable is disconnected from one of the batteries and the meter leads are connected between the battery post and the cable end-there are Youtube videos on this. The normal draws for fridge control and smoke/CO alarms should be below 1 amp.
* Are the batteries good/bad? Many auto parts stores and battery sellers can check your batteries. Even with new batteries, defects happen. Also, if the batteries were in the unit for months before the sale in a discharged condition, they may have sulfated. This means the batteries have lost some or most of their capacity and must be replaced. The batteries installed by FR (based on forum input and what came in my own unit) are NOT true deep cycle. A "car battery size," or Group 24 deep cycle is typically good for 85 amp/hours. Although batteries should not be discharged below 50% capacity, such a battery should (hypothetically) supply 1 amp for 85 hours, two would be 170 hrs. If we extrapolate these numbers, the fridge and CO detectors should run for weeks before the batteries are discharged. The factory batteries are "dual-purpose." This is industry double-talk for a cranking battery (not designed for long discharge/recharge cycling) labeled as being suitable for deep cycle use. The actual amp/hr rates for such batteries is usually only 45-50 amp/hrs. This is done because cranking batteries are 1/2 cost of deep cycles.
The battery is my unit, which sat on the dealer's lot almost a year was badly sulfated. Rather than go through the hassle of getting it replaced with an inferior (dual-purpose) I bought a true deep cycle at Sam's club.
* How much charge is the solar system providing? 200 watts should provide 6-7 amps charge rate per battery in good sun conditions. This should more than keep up with your power usage. If your unit does not display the status of the solar system you can check this with the previously mentioned multimeter. With the solar panels connected and "on" the voltage at the batteries should be approx 13-15 volts. We have a 100W panel and it keeps our battery charged and provides enough power for lights, fridge, detectors, water pump, fans, computers, etc.
When diagnosing electrical problems everything must be checked, but my money is on bad batteries.