Its not a question. Its already an answer to my question: why my implementation of MembershipProvider.UpdateUser() does not affect any changes in ArcGIS Server Manager (clicking 'Save' button on 'Edit user' form does not work)?
I checked UpdateUser() method on all possible situation but not there was a problem. In my case I set MembersihpUser.PasswordQuestion = "" and this raised problems. It looks that you have to set PasswordQuestion for something not empty, like in Esri's sample implementation:
user = new MembershipUser(
"Secret Question", //passwordQuestion field
Maybe it help someone.