I have an Alcatel One Touch 2001 that goes off randomly. I found that the issue is the battery is loose and loses contact inside the phone even though the cover is on properly. The phone gets flexed or squeezed when in a pocket or purse.
The trick to fixing it is to add some padding between the battery and the back cover. I folded a strip of paper to make the spacer, took the back cover off and let the paper sit on the center of the battery. The cover should be more snug now.
I used this trick because it solved similar issues I had with old Nokia phones. It may work with any brand and model phone with a loose battery. If your battery is swollen or dented you should replace it. It should be flat on the back and front and no corrosion or water marks.
Please let me know in the comments if this works for you too.
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