Hi there, @JoanChanning.
Allow me to share some details about what happened during the migration process from QuickBooks Desktop (QBDT) to QuickBooks Online (QBO).
When exporting your QBDT information to QBO, there is some information that isn't included. The reconciled transaction is one of them. As a workaround, you can do the monthly reconciliation on the accounts like what you're doing now.
However, if the bank transactions have been reconciled in QBO and it keeps on downloading duplicate transactions, I'd suggest excluding and deleting them by batch on the Banking page. Also, just in case it's been showing more duplicate transactions even after deleting the first one, I'd recommend contacting our Customer Care Team to check further if there's an occurring bank connection issue.
For a more comprehensive list of the limitations of exporting process, you may check out this article: What to expect when you switch from QuickBooks Desktop to QuickBooks Online.
To resolve any reconciliation concerns, you may visit this article: Reconcile an account for multiple months or years of transactions and financial statements.
I'll be around if you have other questions or concerns. Please don't hesitate to let me know in the comment section. Take care.