What do you think about the functions of が and を, in the first place? "I wasn't sure if I can use を here, well, then, I'll try to use が instead!"?? (Sorry if this sounds sarcastic, but it seems like so to me.)
This clearly shows that my presumption "You don't seem to understand the meanings/definitions of subject and object" is correct. 故障や整備が責任を持つ means "faults and maintenance take responsibility". Read more carefully Morphling-san's explanation.通信網の故障や整備が (communication network faults and maintenance etc.)
責任を持つ (takes responsibility)
When the verb is 引き受ける, 整備を is correct. But, as for the verb 持つ, the object 責任 is already stated. You can't use two をs, thus, you need to use another paticle for 責任を持つ. Look up dictionary.