Hi Kristi,
The list shown under the "add fields" tab refers to items that have a relationship with the table the current screen is built off (i.e. when you select an item in the dropdown it will save to the table). The two dropdowns added from "add object" however aren't linked to your table so if you created a dropdown from this option and, for example, created a new table and entered option1, option2 and option3 as options it can't save the selection to the current record as there isn't a link in the table.
In the example below I created a sample grid to show the information and a simple input form. The field named unlinked was created using a dropdown object which is unlinked to my main "testing" table. No matter what option is selected here it can't save the selection to the record unlike the two fields called linked. The reason that your two dropdowns retain the information on a different record is in fact not because it is saving for all records but because it isn't getting cleared. If you select Save & New you should see the dropdown reset to default and selecting a record you had selected an option in will show this field as blank.
If you already have created a field in your table and want to save the selection to this result you can do this by adding an action to the save button. So for my example above to add unlinked to the table I would use an action like this:
I hope this helps
-Cian