@ Susan
Sounds like you are not exporting all the tables. Make sure you export the following:
{table-prefix}_connections
{table-prefix}_connections_address
{table-prefix}_connections_date
{table-prefix}_connections_email
{table-prefix}_connections_link
{table-prefix}_connections_messenger
{table-prefix}_connections_meta
{table-prefix}_connections_phone
{table-prefix}_connections_social
{table-prefix}_connections_terms
{table-prefix}_connections_term_meta
{table-prefix}_connections_term_relationships
{table-prefix}_connections_term_taxonomy
Using the quick export settings for the SQL file is all that is needed in phpMyAdmin.
Before you reimport, make sure you drop the existing tables otherwise the term parent/child relationships will not be maintained due to the autoincrementing of the term ID column.
Hope that helps!
