"Cannot get mail - The connection to the server failed" on iPhone and iPad

Yahoo does NOT require an App Specific Password for Apple Mail. On the same FAQ page you've linked to, under the section More information on specific third-party platforms it says:

Access mail via Apple iOS

Remove your Yahoo account and re-add it to the Apple email app on your mobile device. When you re-add the account, look for the Yahoo provider logo to trigger the secure sign-in method.

Furthermore, under the page about App Specific Passwords, it says they are for "older, third-party email apps (that do not use our Yahoo branded sign-in page) that require you to enter a single password for login credentials." And as indicated above and from my own experience, Apple Mail redirects you to the Yahoo login page.

I've now deleted and added back my Yahoo address to Apple Mail 3 times, all to no avail. It's totally hit and miss when it decides it can connect to the server and when it can't. And I do not have this problem when accessing my Yahoo address thru either the Spark or the Outlook apps, but I prefer the Mail one and would like to see it fixed than have to check two different apps for my emails.

See:

If you can't receive email on your iPhone, iPad, or iPod touch - Apple Support

If you can’t send email on your iPhone, iPad, or iPod touch - Apple Support

Deleting and re-adding your email account is sometimes the easiest way to resolve a problem with a specific Mail account. After deleting the account, perform a forced restart before re-adding the email account to your iPad.

• Delete account:

Settings > Mail > Accounts > [Your Mail Account] > Delete Account

• Force restart the iPad:

Force restart iPad - Apple Support

• Add Mail Account:

Settings > Mail > Add Account

Be aware that some email providers now require the use of App Specific Passwords when accessing mail over IMAP or POP3. If this applies to your email account, you will need to generate a unique password for your iPad email account - that will differ from your normal Account Password. As examples - AOL, Yahoo, Google, Microsoft all use App Specific Passwords when using anything other than their own email client Apps.

If you need to generate an App Specific Password, you’ll need to log-in to your Mail Providers account management webpage - using a web browser - and generate the Password from the appropriate account security page.

More information about AOL’s App Specific Passwords can be found here:

https://help.aol.com/articles/allow-apps-that-use-less-secure-sign-in?guccounter=1

For Yahoo, more information can be found here:

https://help.yahoo.com/kb/SLN27791.html

For Gmail:

https://support.google.com/mail/answer/185833?hl=en-GB

Microsoft:

https://support.microsoft.com/en-us/account-billing/using-app-passwords-with-apps-that-don-t-support-two-step-verification-5896ed9b-4263-e681-128a-a6f2979a7944