If you must add or remove columns from a table referenced by a Crystal Report, you need not "re-add" the table in question to "see" your new fields.
After making your changes, select Database | Verify Database.
Crystal will now tell you that the database has been verified. You may also see some messages about "fixing up the report". Let Crystal do it's thing. When it's finished, your new fields will be available in the Field Explorer.
You may notice that later versions of Crystal will detect such a schema change and will offer to "fix" itself up.