Yes to both. The first thing I considered was that I wasn't holding it down long enough. I rarely let my phone go below about 60% charge. I honestly think the button may just be defective but checking options first.
Most similar posts have to do with the phone itself shutting down randomly and not being able to turn it back on. That is not what is happening here. I was manually shutting it off when I went into intensive care. When I pulled the battery and re-booted (to see if it would resolve some of the other issues the phone has been having) was the first time it had been completely shut down in awhile. I still had to run and plug it in to start it back up.