First, you'll want to confirm that you're logged in with private repo access. You can easily do this by clicking on drop down for the board name:
OR, you can visit your dashboard and look at the lock icon in the top right corner to see whether you're logged in with private or public permissions.
If you are logged in with private repo access and you don't see your organization's repos when you're trying to add one, this is likely because the organization has 3rd party app restrictions. You'll want to make sure that Waffle is listed as an approved application in order to maintain access to your organization repositories.
You can go to this link to see if Waffle is listed: https://github.com/settings/connections/applications/b68f04bdff231220a275
If Waffle is approved you will see this page and there should be a green checkmark next to the org Waffle is approved for:
If you don't see Waffle listed there, you will you'll need to log out of Waffle and log back in to be prompted to authorize Waffle and create webhooks. (this only applies if you're an owner in your org) If you're not an owner, you'll want to have one do the steps above.