The CANbus is the data network that ties the cars automotive functions together i.e. all the stuff the car relies on to make it move - ABS, Suspension, Gearbox, Transfer Box, Engine etc....
The way the data works is a packet of information is sent that has a header which says which ECU the information is intended for. Each ECU picks up the packet, reads the header and decides if the information is for them, if it is, it reads it and passes it on, if not it just pushes along down the line to the next ECU in turn...
As an Example, the Dynamic Stability Control system (which is controled via the ABS ECU) relies on information from the EAS system to tell it the current height and attitude of the vehicle, this is combined with the information it received from the Yaw Sensor and the Road speed information from the ABS system.
If you have an ABS sensor failure, it will also render the EAS system inoperative, as the system communicate along the CANbus....
If you know your EAS is working correctly and you have no other faults, I would say it is just the CANbus hiccuping as it has received some odd packets of data along the way....that being said, the Twisted Pair of cables that make up the CANbus have been known corrode at the odd ECU connection, maybe looking at the ABS ECU plug, the EAS ECU plug and etc just to make sure. but the CANbus itself won't cause a massive battery drain I wouldn't think as it is only a data network running at the very most 5V signal at milliamps if anything.
I would be tempted to look at the Final Stage Resistor, the Headlamps Wipers or the ignition switch.
Also using a fuse amp meter thingy (one where you can remove a fuse and place this meter in place of the fuse) to see if you can narrow down which circuit it is coming from.