I have contacted my host provider again. I have got the following reaction:
"The error is possible, because the developers [of CB Connect] did not take into account the MySQL standards, as described here:
bugs.mysql.com/bug.php?id=69336
.
One of the developers of MySQL has explained why "The "Row size too large (> 8126)" error is not a bug. "This behavior is expected because inoodb design
requires the record to fit in the B-tree leaf page and if unsuccessful we return error. During the creation of BLOB or TEXT field we allocate 41 Bytes (dynamic or compressed row format) for the field which is considered for row size calculation. During insertion if the BLOB or TEXT is less than 40 Bytes we store it internally with in these 41 bytes and if it is more than 40 bytes, we store it off page and store 20 Bytes reference to the page.""
I hope this information is useful for you.