iPhone only boots in recovery mode - can't restore



I have a little over 2 year old iPhone 6s. The battery was replaced 3 months ago. It has had little use and is plugged in most of the time.

A few days ago, after I unplugged the iPhone, it restarted repeatedly on its own. I could still boot it up and use it after replugging it. Installing all the available apps updates did not fix the issue.

I tried to install the latest iOS (13.2.3 from 13.2.2) a few times with iTunes but the update never completed. At some point I got the message on my computer that the iPhone couldn't be updated and needed to be restore which I tried several times.

Restores never completed because the software download keeps disconnecting. It looks like the iPhone keeps restarting which reset the restore process. The iPhone now only boots in recovery mode.

Is there anything else I should look for or try?