CRP level should drop to less than one-half of its value on admission after a couple of days of antibiotic therapy, since CRP half-life is less than a day following zero order elimination kinetics. 

Of interest, in a study of serial CRP in severe CAP (1), a CRP ratio >0.5 by day 3 was associated with non-resolving pneumonia ( sensitivity 91%, specificity 55%)   performing significantly better than body temperature or WBC count.  

So if there is any doubt about how a patient is doing clinically, a repeat CRP looking for a drop of greater than on-half after 3-4 days of therapy may be helpful.

Bonus Pearl: Did you know that the half-life of CRP is 19 h?

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Reference

1. Coelho L, Povoa P, Almenda E, et al. Usefulness of C-reactive protein in monitoring the severe community-acquired pneumonia clinical course.  Critical Care 2007;11:R92 https://ccforum.biomedcentral.com/articles/10.1186/cc6105