You might try contacting the donations department to see if someone can help you. I would imagine the church is logging all the EFT transactions. Someone can probably look in a log file and figure out what's happening.
The very strange way that funds transfer works in the United States is that you send a request for the funds to the other bank...then you assume you got the funds. There is no acknowledgement from the other bank. If the other bank doesn't like the transaction, they will later send back an error code saying that the transfer failed. In general, I think this occurs within 4 or 5 days, but it can be a "late return" and be rejected several days later.
The church programmers may have wrapped various error codes into a general "Insufficient Funds" message. There are a whole bunch of different error codes that can be returned. Many of them may not be applicable or rarely applicable and might be wrapped up in a generic message to the end user.
The only way you're going to get to the bottom of this is to have a technical person at the church look at the return codes from the transaction. Hopefully they're staffed to check on such things. It shouldn't take long once they locate the transactions. Whether or not that is easy depends on how the programmers stored such information. This is first-hand experience. At a previous employer, I got to search the transaction logs to answer such client issues and worked to get better error information displayed in our software so I could cut down on the research requests.