Recently, Fiverr notifications of messages have stopped working correctly. It seems the first message from a user gets sent as an email notification, but new messages from the same user don’t get an email notification sent.
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Same thing happens with me
I turned notification on, it works well on my phone but not from pc,
Check your Notification Settings 
I’ve got all 3 boxes checked in the notifications section (“inbox messages”, “order messages” and"order status"). I’ve also enabled “realtime notifications” (not sure if I did that after or before missing the first email notification). But surely that shouldn’t stop email notifications if the checkboxes are checked.