Some foundational info first;
I have had two H batteries that had been discharged to <13v. One was bought as "used once" from a person that had crashed his H. After being told the battery was in good shape I bought it and 3 others that were unused. After receiving the used battery I checked voltage and found it to be at a 12.3V charge state. That pretty much explained why the previous owner crashed his H.
The other deep discharged battery was one that self discharged while my H was lodged high in a pine tree. That particular battery sat in the tree discharging for several days and also discharged to about 12.3 or so volts. Apparently factory H batteries contain a discharge protection safety circuit that limits the amount the battery can be discharged. I know a factory H battery contains a pair of printed circuit boards with quite a few tiny components on them. As I do not use Yuneec's H kit charger I don't know what would have happened had I tried to use it, but using a Hitec X2-400 charger set to a 1/2C charge rate both batteries charged up to full capacity with balanced cells. Later charge cycles used a 1C charge rate to achieve a full, balanced charge state. However, something to note is that neither battery would provide any level of useful flight time afterwards and would discharge very quickly as soon as the load from spinning motors was applied to them. 3-5 minutes was the longest flight time either would provide before discharging to 14.7v.
Most chargers are programmed with a lower cell voltage limit below which they will not charge a lipo battery. Should any cell fall below roughly 3.2v or 3v they are no longer safe to charge at standard charge rates. To have any hope of charging cells over discharged a very low trickle charge rate has to be used to elevate cell voltage high enough for a "normal" charge rate to be used. Bear in mind cells in such a state will likely have sustained damage and not function as well, if at all, as they did prior to being deep discharged. They also become a high safety risk.
I suspect the H kit charger has a similar low cell voltage threshold and will not charge a battery that is either too low in total voltage or too low with individual cell voltages. We should understand that Yuneec provides the kit charger designed to protect users from their own ignorance in order to avoid product liability lawsuits from people that induce battery explosions and fires though their own ignorance. Something every drone flyer should do when obtaining batteries is check pack and cell voltage states prior to using them for the first time, but they first need to know what the "safe" voltages should be in order to make accurate assessments. They should also periodically check their batteries to assure the battery has not deteriorated to an unsafe state. The best way to do that is to create and maintain a battery log sheet that tracks voltage, charge rates, charge times, mA input, use cycles, and flight times. Doing so can prevent a lot of angst.
I'm going to be quite blunt in the following; Sorry to say it but the fact is, newbies to the "drone world" typically know virtually nothing about the systems and associated components they are about to start using and often don't bother to perform any educational research until after they've destroyed their aircraft or batteries. Usually that research is initiated only after making numerous inflammatory posts in manufacturer and other RC forums demanding a manufacturer replace their aircraft or batteries under warranty at no charge simply because they were stupid. The batteries we employ to power our systems are not tolerant of abuse but there seems to be a segment of the modeling population that thinks (or doesn't think at all) that lipo batteries can be run down until an aircraft falls out of the sky and still be fully functional afterwards. When things go south they say "but I didn't know and the manufacturer should have better informed me". That doesn't work as manufacturers build low voltage warnings into their systems to assure users don't deep discharge their batteries, but users often ignore those warnings and continue flying, despite anything the manufactures state in operating instructions.
For those that don't understand their batteries, a lipo should not be discharged below 3.2v/cell, with that measurement taken with the battery "under load". Under load means with the motors spinning and ideally during a climb. The total pack voltage should measure 3.2v, minimum, times the number of cells in the pack. Battery voltage measured with no load applied is a false voltage as voltage rebounds several tenth's of a volt after the load is removed. After a period of time cooling off the voltage will rebound a little further. If we ever obtain a 4s battery with a voltage of 12.8v, exactly 3.2v/cell, we can be pretty certain it had been discharged well below that point as the voltage will have rebounded to some extent over time. Personally, I would be highly suspicious of any 4s battery having a voltage of 14v or lower.
The primary message I'm trying to get across with all of the above is to get people to learn more about their systems and the components in them that will be relied upon. They will often find they will have to expand their research beyond the common RC or drone manufacturer forums to obtain the best comprehension of products they will be using. The more they learn the better they will understand what is happening, how and why things work, and why some things may not work as they think they should. The increased knowledge and understanding will make their activities safer and contribute greatly to extending the life of their systems.