Dear Camimac,
I have also had this problem especially with knit shirts, some lables saying 'no chlorine bleach'. I have never been able to get all of them out.
I am thinking to look to see where these stains are located. Since mine are on the front and/or sleeves I must assume it's a food stain even a 'dot' which got on them and might be either tomato sauce, tomato or oil (espeically if I didn't notice it prior to washing). I don't know about cleaning out the washer, but it's worth a try and I will also do a vinegar cleaning.
Usually if the shirt is not permapress or polyester they can be spot cleaned, then washed & bleached successfully. The problem of getting them out of knits is another story. I've even tried lemon and putting them in the sun. Seems to help on some but not on others.
Eventually I come to the conclusion that in order to wear them I must 'paint' them using acrylic craft paint. I did this with a knit shirt that I loved and didn't want to cast off and got many more years of wear.
Funny this doesn't seem to happen with other colors very often. My sugestion (even to myself) is to wear an apron when I am cooking or preparing food, and to be concious of how I eat. Either that or change my shirt beforehand.
Sorry there isn't a better solution tip at this time and I hope the vinegar trick works as well as any other helpful tips that you get. Keep me updated too if you do discover a helpful tip. Believe me, I have tried just about every product I could think of using with some stains being more resistant than others. Good luck. cy