The RFR's battery monitor is not always accurate. There is a known glitch in programming that cannot account for various differences in batteries. Many RFRs will look like they drain batteries quickly when they actually will continue to operate for a normal length of time with the indicator at empty. This is normal and does not require repair.
ETC recommends using rechargeable batteries. As with any rechargeable battery, these provide the best source of power and longest operating life when allowed to be fully discharged and then fully charged. Most users simply use the RFR and then plug it back into the recharger when done - not allowing for the batteries to fully discharge. This type of use will limit the life of the batteries to 3 - 6 months. Best practice is to either have two sets of batteries and a charging system that first discharges then fully charges the batteries each time they are plugged in (keeping one set in the charger and another in the RFR) or to use the RFR until fully discharged and then fully recharge before the next use.
If the batteries are truly not charging and replacing them does not resolve the problem, it is possible that the bottom 2 case screws have become over-tightened. Due to the length of the screws, if they are over-tightened they may make contact with and ground out to the chassis. If long screws are found, they can be removed or replaced with ETC Part# HWM1036, M3 x 0.5 x 4mm