I contact Intuit support and after few exchanges with them, they tell me a way to retrieve the intuit error code associated with UNAVAILABLE NotRefreshedReason.
It is possible to retrieve Intuit error code in field aggrStatusCode when calling getCustomerAccounts, getAccount or getLoginAccounts.
You can then check error codes on this link : https://developer.intuit.com/docs/0020_customeraccountdata/customer_account_data_api/0700_error_codes
Some error codes can be managed with your application users, but other may need account deletion or to contact Intuit support.