A quick Google of the message confirms that this problem is by no means peculiar to Perl.   It is an ODBC issue, and I would first raise the question with “them.”   If you have access to a low-level ODBC debugger/tracer tool, then this would be an excellent time to use it, and it might well be the most informative approach that you can try.

Googling confirms quickly enough that these issues aren’t related to what you might initially suppose:   the query and/or the size of its result-set.   But it could, certainly, be related to some (at the moment, unknown to you...) series of interactions that the driver has with the server during the connection-time handshaking, and those, in my experience, could be absolutely anything.   A PostGres-based custom driver that I once dealt with, for example, actually made some very substantial queries against the system catalog at the beginning of every connection.   I have no idea what it was planning to do with whatever it was receiving, but it sent for the data nonetheless.   Therefore, I would first inquire with the authors of the driver.

it could also be very informative to try other tools against that same driver.   What would Excel do?   MS-Access?   All of these “non-Perl” angles could be informative, and one of them just might hold the key.