Run the following command to see if the any of the "IUse%" column reports 100% full:
# df -ih
If one of those are 100% full then a lack of inodes is the problem and this command will help identify the directories using a large number of inodes:
# for i in /*; do echo $i; find $i |wc -l; done
This can then be narrowed down further by searching the directory with the highest number listed using:
# for i in /<directory name>/*; do echo $i; find $i |wc -l; done
This can then be repeated with a different directory name entry to drill down further if required. Once identified the offending files should be reported to the support team to verify that it is safe to remove them.