While there are numerous reasons why donations may not be coming through from Luminate Online to the Offline CRM (such as the connection is not working properly).  This is assuming the connection is working and that another issue is responsible for the missing transactions.

Make sure to double check the billing name compared to the constituent name.  It is possible that the transactions have in fact synced over, but they have done so on a different user record.  To check, go to:
  1. Data Management -> Fundraising -> Transactions
  2. Look up the transaction by confirmation code, amount, and/or date
  3. Confirm that the billing name is that of the missing transaction and that the user record is a different name.
  4. Check the Offline database for the User record name in the search results, and verify that the transaction has in fact synced.