The help given for this problem is right, but I didn't understand it until I
resolved the issue myself, and wrote it up like this:
Check that the Form object you need the field list for is not really a
query, and then check if the query is missing that new field (column),
because although the table may have your new field, the query won't have it
and that field won't appear in the Field List for the control.
In my case, I thought the control's Field List was pulling from the Table of
the same name as the Form, but in fact the control was formed from a query
made up of fields from several tables, and it was not querying my newly added
table field because the query didn't know about it.
I added the new field/column to the query, and presto! the field from that
table appeared in the Field List.
How did I finally understand what was wrong? When I selected my control, and
clicked on Field List, the Title Bar said Open Issues. The table I thought I
was listing fields from is called Issues, not Open Issues. So then I went
into my database (a freebie, someone's elses) and looked for something called
Open Issues and found a query by that name. And this query was not pulling
from my field called Resolution in the Issues table. So I added it.