after updating with the new version, emails from my second email address are no longer coming through
If the account is an IMAP or Exchange account, you can remove the account from eM Client, then add it again.
If the account is setup as POP3, you want to move all your message, calendar and contact data for that account to Local Folders before deleting the account. Otherwise deleting a POP3 account will delete all your data.
To do this go to Menu > Tools > Accounts.
Before deleting accounts, always make a backup (Menu > File > Backup). If something goes wrong you can just restore (Menu > File > Restore) the previous accounts.