Apparently they do, from the article quoting the US Embassy:
Japanese Immigration officials are aware of the pattern of people staying for 80-90 days as “tourists,” spending a few days in Korea, Guam or some other nearby area and then seeking to re-enter Japan for another 90 days. Persons with such a travel pattern can expect to face questions at Japanese Immigration and may be denied entry with the suspicion that they have been or will work illegally in Japan. In that Japanese Immigration records are computerized, a “lost” passport does not serve to mask long stays in Japan.