Why can't NORX produce intermediate auth tags like Keyak can? Why can't NORX produce intermediate auth tags like Keyak can?  Keyak appears quite attractive because of this, but seems to be slow in the absence of hardware acceleration.
The NORX documentation does not specify how to use it for intermediate tags, but I agree with Richie Frame that it could easily support them. Using intermediate tags in sponge-based authenticated encryption was considered by Bertoni et al., SAC 2011, see Section 2.1. Since NORX's mode of operation is derived from the same construction, I see no obvious obstacle.

Note that, on the other hand, Keyak explicitly specifies the concept of a session with intermediate tags, its implementation readily supports them and its security analysis takes them into account.

About the second part of your question, i.e., that Keyak "seems to be slow in the absence of hardware acceleration", there is no objective reason to believe so, since Keyak with its 12 rounds and full-state absorbing should be at least twice faster than SHAKE128. For instance, our current benchmarks confirm the comment of Biv, as Ocean Keyak takes about 1.8 cycles/byte on Haswell on a single core.

Disclaimer: I am one of the co-designers of Keyak.