Scan OCR does not recognize scanned text messages

My guess is that your documents are already searchable text. The imported text messages are seen as images. If Adobe senses that the document (as a whole) is already searchable, it considers the page "done." As such subsequent OCR processing cannot be done on those pages.

You do not mention what your OS is, but if it's Mac, there is one potential option available to you: Open up Apple's Preview and from the File menu, select Selection -> from Selection. This will give you a cross-hair that you can marquee across the text messages. When this opens up in Preview, it will already be searchable/selectable. You can then copy and paste this data somewhere in your document, perhaps as new pages at the end, perhaps you could title it "Screenshot #2 from page 4" kind of thing.

If you are on a PC, I suggest you see if there is a comparable feature.

Not perfect, but it is a limitation of Acrobat.