Yahoo/AOL/AT&T and Verizon are all using Yahoo's server internally. In addition they have set a very low limit of 4 connections per email account across all devices. In comparison Google has a limit of 15 connections.

This means that even if a particular email client, including mobile clients, is only using 1 connection, you will still only be able to have 4 clients connected to your email account at the same time.

Mailbird as a result is limited to 1 connection for those accounts, but other clients may use more connections and so still prevent Mailbird from being able to connect to the server.

Unfortunately there is nothing Mailbird can do about this. Instead the only solution is to limit the number of devices and connections that at the same time connect to any of those accounts in Mailbird. Most clients have a setting somewhere to set the number of connections they use.