I concur with @JeffSchwenk, MAS makes extensive use of work tables for processing and reporting. Depending upon the size of the overall company database, particularly in history files, work tables and other temporary files could grow quite large during a particular reporting process. As Jeff points out, the amount of free space needed on the drive is proportionate to the size of the data in use. 40 GB sounds like a lot, particularly for an old coot like me who remembers when 50 MB was huge! Today, we can fill a 1 TB drive with VM's from a few projects.
Time to expand their amount of free space.
BTW, kudo's to the IT Company for employing good monitoring processes to identify a potential problem before it grows teeth enough to bite!