MS-Access vba sql update where not working
Its happening because variable name is not correctly placed inside update code and as both column name and variable name are same so according to your current code you are updating all the records.

Try this

sqlcmd = "UPDATE 1_tbl_Memberships SET [1_tbl_Memberships].Member =
No WHERE [1_tbl_Memberships].GroupMembershipID = "&amp; GroupMembershipID &amp;""


http://msdn.microsoft.com/en-us/library/office/aa212163(v=office.11).aspx