Though perms may be a good solution to lackluster pregnancy hair, they might not be the best solution (via WebMD). Permanents contain some pretty harsh chemicals, which may have the potential to be absorbed into your skin, and a possibility of crossing through the placenta to your baby. They can also damage your hair, which is why anyone — pregnant or not — should think twice before getting a perm. 

On top of this, your immune system operates at a lower caliber when pregnant and you don't have the same ability to fight off infection or foreign substances. Your skin becomes more sensitive, and even if you've permed your hair before, your body may react a little differently when pregnant.

The problem is that like with so many other things in pregnancy, there aren't many studies done on perms while pregnant, simply because most pregnant people don't want to participate in studies during pregnancy (via American College of Obstetricians and Gynecologists).