In K-9 Mail 5.800 the “pull to refresh” pattern is used to check for new messages.
Manually sync a folder
Swipe down on the list of messages. Once the circular progress indicator is fully visible release your finger and K-9 Mail will sync this folder.
Manually sync an account
Open the side drawer, swipe down on the list of folders. Once the circular progress indicator is fully visible release your finger and K-9 Mail will sync this account.
Manually sync all accounts
Open the side drawer, tap the lower half of the colored header element to switch to the account list, then swipe down on the list of account. Once the circular progress indicator is fully visible release your finger and K-9 Mail will sync all accounts.
Future
We’re aware that not everyone likes the “pull to refresh” pattern. We plan to bring back buttons or menu entries to refresh a folder/account/all accounts.