Slippage Under Load [New Bike] I got a new bike a three or four weeks ago and have noticed the issue arise this last week or two.  

When I'm going up a hill (or any heavy load), my gears will slip.  I don't think it's moving gears, it just seems to slip a bit.  My pedals will lose tension as I hear it slip, then will regain traction about a half a crank later.

This happens pretty regularly while pedaling in low gear, maybe once or twice a minute.
If the bike is three or four weeks old it is most likely due for an initial readjustment. It takes a few weeks for the cables to stretch a bit and the derailleurs and springs to seat. This is why most shops want you to return the bike after a month or so to retorque the hardware and readjust the shifters usually for free.