Hotend Doesn't Hold Temperature

Attached is a graph of my most recent attempt.  I stopped it when it got down to 185C, which was already 15 degrees below target.

No LED flicker.  The wires going into the heater look solid.  I just started a PID tune and I'll test it again after I enter the new values.

I've been thinking of upgrading to an E3D and this is a good excuse to do it.  But I wanted to make sure that the problem isn't something else.  What are "PSU" issues?

I tried turning the bed temp. off during the print to see if that would allow more power to flow to the extruder.  It seemed to help initially but then the extruder temp. kept dropping anyway (see attached graph).  If I do need to replace my PSU, what would you recommend I buy?  Also, which leeds tend to get hot, is it something I could solder myself?

Thanks for all the great advice!

The best thing I would think to do is start eliminating possibilities, like Ward says test the thermistor... insert a cold extrusion gcode in a file to print then let it go... I would think the thermistor is good though otherwise you peek would have melted and other problems would have shown up. If you have a multi meter connect some extra wires to the hotend heater(at the board) and monitor the voltage on it while printing this will tell you a lot.

Thank you everyone for chiming in.  I played around with the print speed and bed on/off a little and I could definitely see a correlation between nozzle temp. and bed on/off as well as extrusion speed.  If I slowed down the print, the nozzle temp. went back up.  But then it would start falling again 5 minutes later despite the slower speed.

I will get my multimeter and try all of the suggestions tomorrow.  Need some sleep for now.  Thanks again.

Solved!  You all were correct, just needed troubleshooting with a multimeter.

The board was putting out a constant 12.3V to the hot end even when the hot end lost heat.  When I checked the voltage at the hot end, it was intermittent.  I found out that at a very specific point in the wire going to the hot end, the wire must have had a break.  When I wiggled just that part of the wire, connectivity went to zero.  So I cut out the bad section, soldered a piece of wire in, taped it up and closed everything off, and now it is working perfectly!

Thanks again everyone for helping.  It would have taken me a long time to arrive at this conclusion on my own.  Who would have thought a wire could break on the inside when it looks perfectly normal on the outside!