With a great help of Frank, there is a solution for this problem.
If you execute the next query in your database (for instance in phpMyadmin), you can solve this problem:
ALTER TABLE files MODIFY file LONGBLOB NOT NULL;
Please note: already uploaded files won't be changed by this update, so you have to upload the files again after this update. Then everything works great!
This fix is tested on 0.9.6c and 0.9.7RC1 on php4&5 and mysql4&5.