Well, I figured out what was wrong and fixed it. Here's what happened:
I contacted Xantrex and they've been walking me through some troubleshooting. The latest thing they wanted me to do was to test the cable since they thought that might be the problem.
To test the cable, I just unplugged the controller from the wall and plugged it directly into the inverter. That didn't fix anything. But, I thought maybe the cable coming directly out of the controller is bad. So, I opened up the controller to see if I could replace that cable. I couldn't and I put the controller back together. When I plugged it in, it worked without the "AL1" code! Strange. Also, when pushing the buttons, I noticed that now the "Select" button clicks. It didn't do that before. Previously it was kind of mushy, even though it worked. Plus, now by holding in the select button, I was able to make the AL1 code come up, basically replicating the earlier behavior.
So, to figure out what happened, I took the controller back apart and noticed that if I misaligned the button that's directly on the circuit board a little from the external button, it remains clicked in and mushy when the board is put back together. So, I think it was always misaligned ever since it was installed but had just enough play in it that it worked until cold/heat expansion, jostling, or something else pushed it over the edge and caused it close the button circuit all the time, thus causing my problem.
Now I'm also able to change the AL1 code to AL0 by clicking the Select button when the code is showing. I wonder what that code does? There's nothing in the manual about it but, as mentioned in the thread from the other Xantrex product manual, it might turn off or on the alarm. I'll play with it and figure that out.
Thanks to everyone who responded with ideas.