Chosen Solution
So, I recently replaced the screen on my iPhone 4. Everything went fine. Then the phone stopped keeping the proper time and would shut down randomly. I have spare parts laying around, so I tried different parts. I have two separate logistic boards and screens - both do exactly this while swapping them and interchanging them. Any reason behind this? Picture of the issue: https://ibb.co/ePBcfv
That seems to be a screen cable damage. Look closely for any tear or damage on the cable ribbon or connector