ARLINGTON -- Marlon Byrd made his point in the clubhouse after a 9-7 loss to the White Sox Saturday when he was asked what would happen if the Rangers' pitchers could stay healthy in the second half.

"We'll be in the playoffs," Byrd said. "Guaranteed."

The Rangers' pitchers aren't healthy. The club has a half-dozen starters on the disabled list, and Kevin Millwood is trying to battle a series of nagging injuries that have rendered him less than his best.

Millwood, who has been tending to a strained groin muscle all week, insisted he was fine Saturday night, but his manager said something different after the Rangers' No. 1 starter allowed five runs in 5 1/3 innings and lost to White Sox left-hander John Danks at Rangers Ballpark in Arlington.

"People out there don't realize he's fighting injuries and fighting the hurt," Texas skipper Ron Washington said. "But he's a professional and won't use anything as an excuse. He wasn't as sharp as we'd like to have him, but he hung in there and was able to fight his way into the sixth. When he left the game, we still had a chance. He fought like the warrior he is."

But that didn't keep Millwood from dropping to 6-5 with a 5.11 ERA after 18 starts on the season.

"It's frustrating," he said. "We've been playing well and we made a huge comeback from where we were earlier this season, but I want to contribute more."

The Rangers trailed 5-2 after six and 8-2 going into the bottom of the eighth before almost pulling this one out against Danks and three relievers. The Rangers scored two in the eighth and -- after the White Sox scored one -- three more in the ninth. They even got Josh Hamilton to the plate as the tying run with two outs, but he grounded out to end the game.

"Once again, we played nine innings," Washington said. "We tried to make it exciting at the end and tried to pull it off, we just didn't do it."

Ian Kinsler, after going hitless in his first three at-bats, helped fuel the Rangers' comeback with a double in the eighth and a single in the ninth to extend his hitting streak to 24 games.

Kinsler's hitting streak is the longest of his career, the longest in the Major Leagues this season and tied for the third longest in Rangers history. Gabe Kapler had a 28-game hitting streak in 2000, Michael Young hit in 25 straight in 2005 and Mickey Rivers had a 24-game streak in 1980.

"I'm just trying to win games," Kinsler said. "We've got one more left before the break. We're trying to put pressure on the Angels and come back strong after the All-Star break. I'm just trying to get on base and play hard. If you get hits, you get hits. If you don't, you don't."

Hamilton had a pair of run-scoring singles, giving him at least one RBI in eight straight games. That's one behind the club record of nine straight games set by Kevin Mench in 2006. Hamilton also has at least two RBIs in his past five games and 95 on the season.

But for all the Rangers accomplished offensively and for all they did in the end, this game was decided in the middle innings. While Millwood was fighting through one jam after another, Danks was retiring 14 straight hitters after falling behind 2-1 in the bottom of the third.

Millwood started the game by retiring the first five batters he faced, then allowed 15 of the next 26 to reach base on 10 hits, four walks and one hit batter. Millwood has now allowed 36 hits over 20 1/3 innings in his past four starts.

"Physically, everything feels as good as it should," Millwood said. "Nobody is going to feel 100 percent at this point. I don't have anything keeping me from competing. I just walked too many guys. When you face a lineup like that and give away free passes, it makes life much harder. When you walk guys, it gets your pitch count up and gives them free baserunners. You don't see many guys walking guys and throwing a good game."

Millwood faced bases-loaded jams in the second and third innings and allowed just one run. That enabled him to take a 2-1 lead into the fifth, but the White Sox tied it on a triple by Jermaine Dye and a sacrifice fly by Jim Thome.

Chicago then started the sixth with Alexei Ramirez reaching on a bunt hit and Orlando Cabrera drawing a walk. Toby Hall bunted the runners over, and Carlos Quentin followed with a two-run single to left, giving the White Sox a 4-2 lead. Quentin went to second on the throw to the plate and scored on a single by Dye that brought Millwood's night to an end.

Now Millwood gets five days off with the All-Star break and then pitches the first game back against the Twins on Friday. He is still the Rangers' No. 1 starter, even if he's not 100 percent physically.

"I just need him to take care of himself during the break and come back healthy," Washington said. "If he does that, he'll do what he does best -- pitch innings. He's going to be fine. He's going to be there in the end."