Oh boy this could be a number of issues. I would have to start this with some questions.
What model is it?
Does it hold or show a full charge before restarting or on home screen?
Does it restart back to the home screen? Lock screen? Apple or iTunes logo?
When you plug it in does it show the battery charging or blinking?
Does it reboot only when the charger is plug in or before?
Must you leave it plugged in to function?
Based off the comments above, I would say it is one of 3 thing.
-You need a new battery which is not uncommon for iPhone 5 and below.
-You have a little bit of water damage on the logic board.
-You have a Jammed power button.
-I would normally say charger port to, but you said it was recognizing the charger.
Please send me some answers, I am happy to help!