When forwarding or folder rules no longer work (c.v. type with reply message) check this information:
The public folder mailbox is like a user mailbox, so with limits on receiving and blocking send messages if a certain quota is reached.

To change the quotas you must first remove the default quota option from:
ECP -> Public Folders -> Public Folder Mailboxes -> (aprire mailbox) -> Usage -> Customize quota

To change all the values that affect the quotas you have to do from the exchange command line:

Set-Mailbox -Identity "Public Folder Mailbox" -PublicFolder -ProhibitSendQuota 100GB
Set-Mailbox -Identity "Public Folder Mailbox" -PublicFolder -ProhibitSendReceiveQuota 100GB
Set-Mailbox -Identity "Public Folder Mailbox" -PublicFolder -RecoverableItemsQuota 100GB
Set-Mailbox -Identity "Public Folder Mailbox" -PublicFolder -RecoverableItemsWarningQuota 100GB
Set-Mailbox -Identity "Public Folder Mailbox" -PublicFolder -IssueWarningQuota 100GB
Set-Mailbox -Identity "Public Folder Mailbox" -PublicFolder -RulesQuota 256KB

Eventually (but they are already high by default) you can also change the values of "ArchiveQuota" and "ArchiveWarningQuota".