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Do you have any taskillers? battery apps? ram apps?
This should explain how Stamina Mode work
http://talk.sonymobile.com/t5/FAQ/Battery-time-and-enhancement-features/m-p/347874#U347874
This goes for both, please do repair your phone with SUS or PCC and report back
Bridge (for Mac)
Alternatives on How to backup Xperias
i did update with sus bt still no luck.
This seems like a harware issue. contact your local service center