Restarts / shutdown unexpectedly

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My Xperia SP with os4.3 version restarts or shutdown unexpectedly when any call comes or launches any app. This happens only when the battery level is below 60%. Also the battery drains very fast. I used to get a back-up maximum of 6 hrs only. I don't have too much calls. Only few calls and full time internet for mails, Whatsapp, and Facebook. While the battery level is low and its on charging, then the phone don't don't have any auto shutdown or auto restarting problem.
I approched the service centre to change the battery, but the technician says that the battery is perfectly ok and the problem could be with the main board. Its very costly too. If its the problem with the main board, then why the problem is there only when the battery is low.?
Please assist me, what should I do rectify it? Do I need to change the board or its the problem with the battery?

[_alexdon_]

I would suggest you to check with other SIM cards too,occasional restarts could be related to a faulty SIM.

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Yes. I had tried by changing the SIM card, removing the memory card and repairing the OS with Sony PC Companion also. But still the fault remains. 

If it is the problem with the SIM card, then I believe the problem must arise at any time at any battery level situation. But here the fault is happening only when the battery level is below 60%. Even if the battery level is low and the phone is on charging, then there is no issues at all.

[_alexdon_]

You should stop by a sony service:

http://www.sonymobile.com/global-en/support/contact-us/

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At service centre they says it will cost more than Rs.10000 to replace the board whereas a new Xperia SP is costing only Rs.13,000 in online purchase. Also the replacement will take too much time (more than 2 weeks) as the spare part is not available there. In this circumstances why should and how should I repair my phone?

Then I done some experiments. I tried with another SIM, but still the fault remains the same.
Then I tried without a SIM. Now there is no problem. Working fine without a SIM. So now I'm using my phone like a Tab in WiFi to use WhatsApp untill I purchase a new phone.

All my friends who are / were using Sony phones were facing some sort of issues and all of them quit from Sony.