When is it appropriate to request more effort from a co-author on a funded project?
People's contribution to projects is mainly determined by two factors:


Motivation. This might be career advancement opportunities, reputation advancements, working together with somebody they admire, publications, money, etc.
Ability. Time, knowledge &amp; background, access to literature, access to production tools, equipment, etc.


When somebody is not contributing, they are lacking in either category (or in both). So the first thing you might do, is to inquire in a polite and sensible way where the problem is. Is the co-author lacking ability (time, tools, ...) or motivation? When you know the answer, you can figure out together how this can be resolved.

When you approach this as described above, you can do this immediately. You do not need to wait until some threshold of (un)acceptable behavior has been violated. 

A blunt confrontation rarely delivers anything productive, certainly not in the long run.