Actually, it's difficult to say exactly what causes baby eczema, but here are some things that make it more likely to occur:
- Inheriting the tendency to have it
- Irritants coming in contact with baby's skin, such as rough clothing, harsh detergents
- Heat.

How to prevent and cure it:
Most people use use over-the-counter topical creams such as Funbact-A to treat and prevent baby eczema, but in my opinion, this is rather harsh, so here are some gentle and natural ways to treat and prevent eczema:
1. Always moisturize your baby's skin: Use coconut oil or baby lotion or oil such as Pears immediately after bathing your baby to prevent skin drying out. Apply while the skin is still damp. The great thing about coconut oil is that it also cools the skin and offers your baby relief from itching.
2. Allow ventilation on your baby's skin: Dress your child in smooth natural fabrics, like cotton. Avoid wool and other scratchy materials, which can irritate very sensitive skin. Don't overheat your child by bundling him/her up more than necessary. It's also okay to take off your baby's clothes when the weather is hot.
3. Use mild detergents only: Always use mild detergents to wash your baby's clothes. Mild detergents are those that you can use for colours such as Sunlight.

Source: http://nigerianbaby..com.ng/2016/03/get-rid-of-baby-eczema-naturally.html