Imagine a language that, like Japanese or Persian, expresses a lot of verbs using "do/make" plus a noun (English allows this in some contexts: "make a donation", "do a runner"). But, unlike Japanese or Persian, let's suppose this language has gender - like Kurmanji, say - and adjectives that agree with the noun in gender. In such a case, it would seem reasonable to have at least some adverbs expressed as adjectives agreeing with the verb's noun: "make frequent donation" for "donate frequently", say. Likewise, ellipsis could be handled with an appropriate pronoun: "I made a donation (masc.) to the library, and he made one (masc.) to a charity."
Now let the forces of phonetic erosion work on the verb phrase for a while, until the former support verb is reduced to a mere suffix attached to the stem (rather like what happened to Latin habere in the development of the future tense in Romance.) Unless the rest of the system has been reworked in the meantime for some reason, the result should be a language in which adverbs and pro-verbs agree in gender with verbs.
Is there any language that has done this? If not, why not?