I have seen this problem a number of times on different devices, with the following causes (and solutions) for the problem:
Wrong authentication method: at the bottom of the advanced part of the Mail account settings: if the authentication is "password", and the server prefers another method - typically MD5 challenge responce or NTLM (Exchange servers), the password isn't sent in the form expected by the server, resulting in the misleading error message: "missing password". Solution: change the authentication method to a method understood by the server. No need to recreate the account.
TLS/SSL turned off: also at the bottom of the Mail account preferences advanced part: many modern email services enforce encrypted delivery/transport of email, if is turned off the solution may be to turn it back on (or vice versa) - still no need to recreate the account.
Account created with an alias address - not the primary account: many email services allows the user to use the same account with different sending addresses, and Apple allows the user to create accounts using an alias address. This appears to sometimes confuse Apple Mail, resulting an account that can be validated without problems in Mail Preferences, but gives problems when used in Apple Mail. Solution: create the account using the email addreess given by the email supplier, add the preferred sending adresses by selecting the Email field in the Mail Preferences, and select the address that you primarely want to use when sending. This requires the mail account to be deleted and recreated.
In some cases a bad/intermediate network connection, appear to result in one or more email settings getting changed resulting in the problem. This normally occurs when fetching email from the server, resulting in the preferences for sending email still working fine.