I don't know if this is a kodi issue or a Flirc issue, but I will try here first.

Last night my Pi3 with kodi (openelec) froze, where I had to do a hard reboot. After that my Harmony Ultimate would not work properly. Kodi no longer responded to the direction keys or the select key. It would back a noise if I pushed the Back button, and would respond to the Page Up and Page down buttons on the screens.

I downloaded the updated Flirc app and updated the firmware, re-programmed the direction and select buttons, and returned the Flirc to the Pi 3, but the problem still persists. Is there anything else I can do, or is this a Kodi issue?

You can test your Flirc by plugging it to your PC/Mac and start some app which you can control with direction buttons and enter. Then just press buttons on the remote. If the app responds properly, then the Flirc is OK and the issue is with your Kodi installation.

Good thinking. I gave it a whirl, and it worked fine with kodi on my Surface Pro tablet. So I'm going to have to fix the kodi installation. Unfortunately, the backups I made in the summer seem to be gone. I'll have to go on the kodi forum to see if there's a fix that doesn't require a full reinstallation.

Thanks for the help :)