That happens when the battery ages. It sounds to me, you might need a new battery. The battery is not `broken', it's quite likely that is has simple gone through sufficiently many charge cycles.
LiIon batteries usually last 500-1000 cycles, so your battery giving out after about 750 charge cycles sounds normal. The capacity lost doesn't just depend on number of charge cycles, but also the ambient temperature: if you live further south, your battery will lose capacity faster.