A bicartesian closed category of strict complete partial orders (Hask)
Yes, it's impossible to have a nondegenerate CCC with general recursion and categorical coproducts. The standard reference for this is:


  H. Huwig and A. Poigne. A note on inconsistencies caused by fixpoints  in a cartesian closed category. Theoretical Computer Science, 73:101–112, 1990.


However, I and (most of the other people I've met) learned about it from Achim Jung and Samson Abramsky's handbook chapter Domain Theory, which they have kindly made available for free. 

Most of the categories of domains that people work with are subcategories of DCPO, the category of predomains and continuous functions on them. Since predomains do not necessarily have a least fixed point, this category is a bi-CCC, but fixed points only exist for functions into domains. 

On page 46 of these notes, there is a big table telling you which subcategory of DCPO different constructions exist in.