First, go into “Settings” then “Notifications” and make sure "Current Conditions" is checked and "Auto Refresh" is enabled.
Below that, make sure that "Ongoing notification" is checked, otherwise the notification will be cleared whenever notifications are cleared and won't reappear until the app launched next.
Third, make sure that the “Temperature color” setting is set to a color that you can see against your notification area (not black against a black background, for example).
Finally, check the Notifications "Location" setting and make sure that the location is set to a location that is currently in your list, not a location that has been previously removed.
If none of the above appears to help, the next thing to try would be to increase the “Notification priority” setting from its default of "Normal" to "High" or "Maximum" to increase 1Weather's priority in the notification hierarchy on the device.