In your post on Seasoning Stainless Steel, you say to "wash in warm water with a small amount of dish soap and dry immediately."  I thought that soap would dissolve the fat, so you would damage the coating if you use it.
- Comment^*

Seasoning in this sense involves heating oil in a frying pan, or other cooking surface, to form a non-stick layer (see Seasoning Frying Pans).  The oil undergoes a process of polymerization which forms a shellac-like compound.  Because of this chemical process, the fat is no longer actually fat, per se, and is more like a plastic.  According to McGee, 'the combination of heat, metal, and air oxidizes the fatty acids and encourages them to bond to each other "polymerize" to form a dense, hard, dry layer.  ... Highly unsaturated oils - soy oil, corn oil - are especially prone to oxidation and polymerization.'  Add to that list flaxseed oil.  As the food grade equivalent of linseed oil which is used for varnish, flaxseed oil gives what some feel is the most durable seasoned surface.

Since the oil has polymerized, it is no longer as susceptible to the surfactant properties of soap.  A mild dish soap solution and cleaning with a soft cloth will not damage the seasoning.  My guess is that if your seasoning is coming off during washing in a mild soap solution any of a number of factors may be the cause:

• A strong soap solution, or dishwashing detergent is being being used.  Dishwashing detergents are more harsh and have a higher pH.
• The pan is being left to soak.  Over time water will penetrate and cause rusting on cast iron, which will cause the seasoning to come off.
• Scrubbing too hard or with an abrasive pad.  If necessary, you can rub a little table salt on the moist surface of the pan and rub it with a dish cloth to help remove stubborn material.  This will abrade the seasoning, but not as bad as say steel wool.
• Using the wrong oil.  Oils that are low in unsaturated fats will not form the necessary polymers as readily.
• Not heating the pan to a high enough temperature or for a long enough time for polymerization to happen.

A properly seasoned pan will not suffer from a quick wash in a mild dish soap solution.

For another interesting article on this subject, see Chemistry of Cast Iron Seasoning: A Science-Based How-To.

^* This post is based on a comment received from 'Svensson' on the prior Seasoning Stainless Steel entry.