You can check SAP note 1901556 for details about all the issues you will potentially encounter and how to solve them.
You can use adapter objects defined in R3AC3 to download customizing data. When it doesn't work, the most common issue is in ECC table CRMATAB, there's no proper entries. eg. if you're to download DNL_CUST_KTOKD - account group, the relevant table T077D and T077X must exist in CRMATAB on ERP.
If this table is empty or not having the relevant entry for the adapter object you're using, you can run report SMOF_FILL_CRMATAB in CRM to fill this R3 table.
When you run this report, you need to fill in the following parameter:
Source Site Name --- R3 system site
Objectname ----- the adapter object
(if table CRMATAB is empty and you want to fill in entries for all the adapter objects, you can also check the checkbox 'All objects'.)
But report SMOF_FILL_CRMATAB requires some special authorization.
Note 1498111 explains the specific authorization required for the initial download of customizing object. Please also note that the authorizations described in this note are not covered by SAP_ALL - so even if your user has authorization SAP_ALL, the additional authorization is required. It must be added to the user defined in SM59 of the CRM that connects to ECC system - this user which is maintianed in SU01 of the ECC. Also, it should be added to the user defined in SM59 of the ECC that connects to the CRM destination (this time in SU01 of the CRM).
In some cases, the report SMOF_FILL_CRMATAB doesn't exist in CRM. In that case, you need to apply note 1501685 to populate this report.
Also, in some ECC systems, there're no function module CRM0_WRITE_CRMATAB. Because report SMOF_FILL_CRMATAB will call ECC FM CRM0_WRITE_CRMATAB remotely, to fill table CRMATAB, when this FM is missing, the report will fail. In that case, you need to apply note 1502607 in ECC to populate FM CRM0_WRITE_CRMATAB.
The above are basically all the issues you will potentially face with table CRMATAB.