I removed all code referencing the IRRemote and uploaded it to the NANO and the clock worked flawlessly for a couple of hours, where it wouldn't run more than a half hour before. So, then I put all the code for the IRRemote back in and uploaded it, and the clock has worked perfectly all weekend. I didn't make any hardware changes or changed the code in any way. The only thing I can think of is some kind of glitch happened when I originally uploaded the code. I just know if I ever run across a weird problem like this again, one of the first things I'll do is reupload the program. I want to give my sincere thanks to everybody who tried to help me with this.
TomGeorge: To answer a couple of your questions - it is powered by a 12VDC plug in adapter. And, yes, I did measure the output voltage and it was the same before and after the fault. It is a 4 digit display. The only voltage discrepancy I found was at Pin 1 (data in) of the MAX7219. Before the fault I read 2.xx volts, and after the fault I was reading less than 1/2 volt, which I took to mean the Arduino was no longer sending out a data signal. But the clock is now working. I removed all code referencing the IRRemote and uploaded it to the NANO and the clock worked flawlessly for a couple of hours, where it wouldn't run more than a half hour before. So, then I put all the code for the IRRemote back in and uploaded it, and the clock has worked perfectly all weekend. I didn't make any hardware changes or change the code in any way. The only thing I can think of is some kind of glitch happened when I originally uploaded the code. I don't know what else it could be. I do appreciate all the help you and everybody else has given me.