Can you get Netflix on any other devices OK, if you have anything besides the Stick that can get it?
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Have you tried the basic stuff like disconnect the power to the stick and your router for about a minute, if that doesn't work go to the My Apps section and remove the Netflix App, then go to Apps Store and re install the Netflix App again.
Last resort try a factory reset on the stick, but that involves a bit of faffing around setting up the stick again from scratch.