Also I would add a couple of things that have caught me in the past. A quick sanity check that the token is still valid (I set an expiry on a testing token once, that caused me a little bit of chasing my tail).
Also, to test that and double check that everything is OK with what you are attempting to do (and that it is a local problem with postman) have you double checked to ensure what you are trying to do works with the Live API, that is normally my first point of call to make sure there are no other issues.
You can do so by adding '/doc/api/live' after your Canvas URL (e.g. https://example.instructure.com/doc/api/live). Never hurts to double check the basics, if not, would love to see the part of the URL you are using after example.instructure.com/ (as Matt said though, very good policy to black out your Bearer Token.
Hope that helps!
Stuart