Bathroom outlet has poor Continuity, no tripped breakers
Sounds like a loose connection somewhere.  

This outlet may be the culprit, or maybe one upstream.  

Since this outlet was the most recently changed, I would take off the wires and check them with a volt meter so see if you are getting consistent power to that point.  

Then reinstall the outlet and see how it goes.  

From that you should be able to determine the location of the problem.