Exclusively Breastfed baby keeps catching colds

I’ve always heard that breastmilk protects babies by strengthening their immune system. My last baby didn’t get her first cold until she was a year old! My little one is 3 months old and is going on her 3rd cold! She caught her first one at 4 weeks. They’ve have been mild and she recovers quickly. Her doctor isn’t worried, but I’m curious if any others have had their breastfed babies catch every cold they come in contact with! We have 4 kids by the way, so that’s why she keeps getting sick. I just had hoped her breastfeeding would’ve helped.