iPhone 5s apple logo and shutdown, restore worked for 3 weeks

Hi.

I have an iPhone 5S that shows the apple logo for half a second (when i try to turn it on), and shuts down. Then, if i try it again, nothing happens and the iPhone seems to be completelly dead. If i try it again after half an hour or so, it does the same thing, apple logo for 0.5 seconds and shut down, and then dead again for another +/-30 minutes.

I was able to restore it on iTunes. By pressing the power+home button for a while the screen remained black, but the phone was recognised in itunes as being in recovery mode, and i was able to restore it. The iPhone worked fine for about 3 weeks, but now it’s having the exact same issue, so i believe this is an hardware issue. Any suggestion? I tried with a new battery and the result is the same. I have some experience with micro-soldering, but not so much with diagnosing… Thanks in advance!