Why does my iPhone show the apple logo then shuts off

A lot of things can cause a phone to stop or loop during the boot cycle. The key question here is did this happen out of the blue or following a repair, drop or contact with water?

Try these things (if you haven't already) to see if anything helps:

• Try a hard reset (Home & Power button for 10 secs)
• Use a genuine Apple Lightning connector
• Use a genuine Apple charging brick and let it charge overnight
• Try to connect it to different computers (mac/pc if possible) with an updated iTunes
• Change the battery. The battery is the weakest link in the entire phone
• Put the phone in recovery mode (search DFU Mode). Careful, this can reset your data
• Use 3uTools for putting it in and out of Recovery Mode
• Use 3uTools to flash the firmware (you can't downgrade)
• Check the condition of all the flexes (with magnification)
• Disconnect the Front Camera Ribbon from the logic board and reboot your phone
• Disconnect the screen assembly completely and see if iTunes will recognize the phone.

 Otherwise, you may have a logic board issue. If you are uncomfortable doing these steps, consider finding a repair shop to do the troubleshooting. A shop that also does micro-soldering can go deeper if the problem is not modular in nature.