I wouldn't advise the use of an eggshell/satin finish in such cases because the problem you are experiencing is likely due to high levels of UV radiation which is exasperated when using such coatings that have low levels of light deflection.
If you are determined to use such a finish then the general advise with all paints is that you get what you pay for and using a recognised brand, formulated especially for exterior use is the safest bet. Water-based finishes also tend to perform better externally than oil-based alternatives because they maintain flexibility for longer.