Loss of recursion
As the preceding discussions suggest, recursion is a product of the rules that one wishes to set up in order to describe and/or account for structural properties of a given language. Once one’s description contains a rule of the form (1b) then there is recursion. The position we adopted is that there are pragmatic reasons in favor of such a rule, and our main concern was with showing how recursive morphosyntax emerges out of non-recursive structures. But there is also evidence for the opposite development, whereby recursive morphosyntax ceases to exist.
One kind of decline is provided by the development of adpositions. Cross linguistically the most common pathway in which adpositions arise is via the reinterpretation of nouns for body parts or environmental landmarks, forming the head of possessive constructions, as prepositions or postpositions (Heine, Claudi, and Hünnemeyer 1991; Heine 1997b). For example, the phrase (19) is historically a possessive construction consisting of the modifier noun gǀǀu̒ ‘water’ and the head noun !xˡ ā ‘heart’, but the latter has been grammaticalized to a postposition meaning ‘inside’. The earlier syntactic structure of (19) can thus be represented as in (20a) while its present structure takes the form (20b). Note that this is by no means an uncommon example; similar examples can be found in other languages across the world.

In accordance with the rule convention adopted for this example, such cases can be described as ones where a recursive possessive construction of the form (20a) has been grammaticalized to a non-recursive adpositional construction (20b)—that is, as a construction that no longer corresponds to our definition of recursion in (1b).
The second kind of decline is of quite a different nature; it concerns loss of productivity in grammatical constructions: Once a recursive construction is lexicalized to an unanalyzable unit, it loses its recursive nature. For example, English has a recursive [[adjective] noun]-rule. But in adjective–noun compounds, such as darkroom, hothouse, or blackbird, recursion is lost.
To conclude, the languages of the world offer many examples where new recursive constructions arise, but also examples where existing recursive structures can disappear. Loss may only concern individual, lexically determined use patterns, as in the English examples, but it may as well affect more inclusive phrase structures.