The Yawara! manga was written starting in 1986 and lasted until 1993. In the manga, Yawara is actually meant to compete in the 1988 Seoul Olympics:
However, when it was adapted into an anime, which aired from 1989 (after the Seoul Olympics) until 1992, they kept the media contemporary (instead of dating it), they adjusted this to be the 1992 Barcelona Olympics. (Side note: This worked out well for them, as a competitor much like Yawara won in real life in Barcelona that year and received the nickname "Yawara-chan". The more you know!)
Zutto Kimi no Koto ga, however, was not released until 1996, two weeks before the 1996 Atlanta Olympics, hence it was adjusted for this set of Olympic games instead.
It seems that, in each instance, the producers wanted to play somewhat on the publicity of the Olympic games, and by 1996 they were good enough to air their special only weeks ahead of the real thing. There is no in-universe reason for the change here, simply that she was competing at the "upcoming Olympics" in two different time periods (pre- and post-1992).