This is not an AirPort router problem....this is a problem with your Mac's operating system, so you may have better results posting in the Sierra support forum.
The first troubleshooting step to perform.....if you have not already done this.....would be to clean out the history of networks that your Mac has joined in the past, so you can start from a clean slate. To do that....
Open System Preferences (gear icon on the dock)
Open Network
Click on WiFi on the left panel to highlight it
Click the Advanced button at the lower right of the window
Here you will see a listing of all of the networks that the Mac has joined in the past.
Click on the name of a network to highlight it
Click the - (minus) button at the bottom of the list to remove the network listing.
Do the same for all other networks that appear until the list is blank.
Make sure that a check mark in entered in the box that reads "Remember networks this computer has joined".
Click OK
Click Apply in the next window.....(this is an easy step to miss)
Close the windows
Restart your Mac
Connect to the wireless network again from your Mac. You will be asked for the password, but if things are not corrupted in the KeyChain settings, your Mac will remember the password in the future.
If still no luck, the settings for the network in your KeyChain are likely corrupted. Rather than look for an obscure setting and try to make changes....which can be dangerous.....my recommendation would be to rename the wireless network and password on your AirPort routers and try things with those new settings.
If the Mac still cannot remember the network and other devices can.....you will likely need to reinstall the Sierra operating system on the Mac. As mentioned previously, you have a Mac / Sierra issue, so you will likely get a faster and more informed answer if you post in the Sierra support forum which is linked just below. Good luck.
macOS Sierra