Please allow me to explain the situation as per my experience...
The issue is with the battery. AGS is also part of Atlas group and their batteries have had some problems with poor reliability and performance. Secondly I think the battery is too small for the car! When the car is off, some functions are still running and that drains the battery. When the car starts the alternator will pump a high amount of energy into the battery based on its state of discharge and this the battery cannot handle. It hence heats up and also dries up. Get a 65 amp hybrid battery from honda.
Secondly the location of the battery is not to my liking and for some silly reason Honda have installed a cover around it. I believe it is to insulate the battery from the engine bay heat but it might just be cooking the battery.
Thirdly, I am of the opinion that a dry battery should not be used. If it is of a sealed type, then it will simply have a high probability to explode if it also behaves in a poor manner in this car!
Last but most importantly, I am also of the opinion that this issue is the cause of fires in Civics lately. After market lights and electrical accessories may be adding to the problem already being faced by the battery. Lead Acid Batteries produce hydrogen and the rate at which this car empties the battery water, I think it is a recipe for disaster!
Hope this helps.
Drive Safe!