Painting - restaining cabinet doorfronts

We're in the middle of an entire kitchen renovation. We're having doors and drawer fronts made of red oak to match the current cabinets. Our problem is this: We're trying to get the previous stain off (a pickeled white or frost) the cabinet fronts. We sanded first with a100, then a 150 sandpaper, then we used a stripper solution with a stripper brush to try to get the stain out between the grooves of the wood. After wiping down with mineral spirits we've sanded again with 220. The stain hasn't come completely off in alot of the grooves. We've tried to sample stain another similar board and you can see the old stain coming through. Our question is this... can you damage the wood by using the stripper and the stripper brush over and over? Is there another technique that would be more effective? Any recommendations would be very much appreciated. We've spent so much time so far on this project, we don't want to mess it up now!
Thank you, Christina

I believe using the stripper is the best approach to lift out the stain. Laquer thinner might help after washing the stripper off as it lifts oils up. Sanding will take off too much material on veneers but would work on solid woods. Restaining is difficult because impurities go deep. lol .....jeff

Yep, what he ^^^ said.