Blues just seem to have very poor immune systems as well as being poor breeders/producers. This is just "in general" and you may have some that do better than the majority. They are a recessive gene so it takes some inbreeding to get them, which is why the blue rats you see in pet stores have such poor health. It's just not something I recommend doing unless the rats are extremely high quality from a professional breeder and have come from a proven line of healthy rats.

I only have three "blues", one of which is an american blue dwarf dumbo. I'll never breed her as she's about the size of a large mouse. My other Blues aren't even american blue. One is a Blue Agouti(which is a dominant color) and the other is a Double Blue or Silver Blue(undercoat is silver, topcoat is blue, she's pedigreed but is from a questionable breeder). I've only ever bred the Blue Agouti, as he is also pedigreed and his line comes from OFR(Odd Fellows Rattery).