I have had this problem since the series 2. Anyways when I turn off my phone (like being in church) my watch connects to the churches WIFI and apple mail on the watch has a hard time fetching and sending mail. Perhaps a bug. Anyone else?
You cannot send or receive new email using the native Apple Watch Mail App when not connected to your iPhone via bluetooth. Though I've found some exceptions, if your Watch is not connected to your iPhone via Bluetooth but both Watch and iPhone are on the same WiFi network then mail functions. Likewise I have left behind my iPhone on the charger at home and went out only with my cellular Watch and I can receive email but not send. I sure hope full mail functionality is coming in WatchOS 9. Also there are some third party mail apps that do have more functionality for Watch not connected to iPhone like Spark.