One problem related to battery has been reported for the 2005 Honda Civic Hybrid. The most recently reported issues are listed below.
My car is not accelerating properly. Despite the fact that I brought it in to the dealer in about November of 2011, they did not do anything. They claimed it was the way I drove. I've always driven the same way and owned the car for 7 years now. Then, a few months ago, I discovered the reason I lost power was they reprogrammed the car so I lost power! I am sure you are aware of the various lawsuits against Honda for reprogramming the hybrids so that everyone lost about 5 mpg and the battery was less powerful, all so they could make the batteries go past warranty and they would not have to pay to replace them. My car battery has also started to charge when I accelerate, which it is not suppose to do. This is making it difficult to get on the highway. Around here, there are entrances that are stop signs and you wait for a large enough space to get in. My space is getting longer and longer because I am afraid I will get in an accident if I don't have that extra room I need to accelerate up to highway speed (min. 50 mph on this highway).