"to remain in good stead" means to continue in good standing, to continue to be respected, or to be up to date in one's dues when a member of some organization. "Stead" means "standing" as in "place" or "position," socially, or otherwise. The word "stead" is related to "stand," but isn't commonly used much in American English. It is, however, commonly used in words like "instead," "homestead," "steady," "steadfast," etc.