Honda Civic Hybrid battery problems

I have bought a Civic Hybrid in 2007 brand new. The 12 V battery which drives the starter as well as all the elctricity stuff in the car was replaced in 2010. In August it went flat but after re-charge it was OK until this morning when it went flat again. In the past few months I have also experienced occassionally that the IMA indicator suddenly dropped to the level of 2 or 3 lines but shortly returned to the "fully charged" status, not gradually, but with a fast pace.
I wish somebody could explain the relation between the IMA and the starter battery. Can a faulty IMA result in drying the starter battery? Can a faulty starter battery lead to the strange phenomena about the IMA I have described above? Any advice would be much appreciated and sorry for the poor English.