Aircraft System Voltage - "B" Alternator.

What voltage do you see on Pin #3 of the X3 connector on the Fuse Box. 
Measure from the PIN to the Ground plate of the regulator.
You may be Loosing some voltage in the wiring or the ground.

What Brand/Model of battery do you have that doesn't charge above 13.8v ???
- - -
The nominal voltage is 14.2v, but the range is from 13.9 to 14.5v.
There is no adjustment available, and you are within specs.

Hi Bill, I'm seeing 13.94 - 13.94V at the battery terminals and there is no chance that the voltage at pin 3 on the connector is any more. This is all brand new wiring, a gauge larger than specified by rotax.

''The battery is an Earthx ETX 1200, great customer service. The battery charges just fine, but it needs more than 14V to do effective cell balancing. It tries when it reaches 13.9v and a charge rate of less than 2A, but doesn't succeed because the voltage is a fraction  too low. That generates about ten minutes of nuisance alarms on my EFIS. I'm going to have to get a new battery charger just so that I can balance the cells.

The EarthX Users Guide shows that the ETX1200 Standard Charging Voltage is 13.9 to 14.6v . (Page 12)
And indicates on Page 20 that it can sucessfully Charge/Maintain down to 13.3v.

A fully charged ETX1200 battery is considered to be 13.2v.
13.5, according to the chart, indicates you are within 1Ah of Peak Capacity.

Are you having a problem starting the engine or just complaining that the charge rate is low (2A) after starting.
It is unreasonabe to expect a 10-15 amp charge rate after starting if the engine started in the first 5 seconds.
If the engine started with minimal cranking, the battery did not use any significant capacity in the process and does not need much charge to replace what was used.
There are dozens of these batteries being charged by the 13.9v plus Rotax charging systems without complaint.
You may want to discuss this with EarthX directly, but I do not see a problem.

If you wan't to exercise the charging system, Power up the plane, Engine OFF, and wait for the battery to get down to about 12.8-12.9v.
Then start the engine and see what the charging current is, and if it is restored to above 13.2 v in a reasonable time.

EDIT:
I re-read you complaint.  You are getting false alarms from the EathX Battery warning Wire.  PITA!
I once again recommend measuring from X3-3 to the Regulator "B" Ground Plate just to cover all bases.  (14.1v ???)
We are only talking about 0.3v that can be lost in either the Hot OR the Ground cables/connectors.
Then measure from X3-3 to to the Battery Positive Post. (The POST, Not the battery connector). Should be 0.000v (Not 0.100)
And from the Regulator Ground Plate to the Battery Negative Post. (The POST,  Not the battery connector)  Should be 0.000v.

Could this be a problem of overheating the B regulator?  You said you were only running 5 amps.

Apparently these regulators shed unused power as heat so when it's hot it is better to load them up with lights etc. Here is what Vans FTS says.

"The Rotax 912 iS is equipped with two voltage regulators, one for each generator on the engine. These regulators reject any unused electrical power as heat. Allowing the power usage to fall below 7 amps for extended periods of time may damage the regulators, especially on hot days. For this reason, it is recommended to turn on the Avionics Switch, NAV/STROBE Switch and Landing Light Switch once the engine is running. Voltage regulator B provides power to the main bus and is located on top of the fuse box. This regulator is the most susceptible to overheating."

Maybe running too low an idle rpm with all the lights and instruments? Does the problem still exist at higher rpms or decrease voltage drain?