Dunn struck out four times Thursday night, two games after being moved to the No. 5 spot for the second time this season.
"I want to make sure he relaxes a little bit," manager Ozzie Guillen told reporters after Thursday's game. "It's not to punish him. Right now he's a little frustrated. I think we kind of worry about him. You can see him kind of worry about it. After his at-bat he's very down. But I have to continue to play him."
The slugger, who signed a four-year, $56 million deal this offseason, has struggled for all but a week-stretch on the White Sox's previous road trip through Seattle, Anaheim and Oakland. Since then, Dunn has gone 4-for-40 (.100) over his last 12 games.
He is 0-for-33 against left-handed pitching and his 65 strikeouts are tops in the American League. His batting average dropped to .186 after Thursday's game.
"I hope batting him seventh he will get a break and relax a little bit," Guillen said. "Hopefully that works. When he starts swinging the bat better we will move him back to where he's supposed to be."
Dunn has batted in the No. 3 spot 30 times this season, was in the cleanup spot once and has batted fifth 12 times.
Doug Padilla covers the White Sox for ESPNChicago.com.