This seems to have nothing to do with sendmail as such. It's a problem with running out of inodes, period.
Very broadly speaking, you use up one inode in a filesystem every time you create a file, directory, symbolic link, etc. in that filesystem. You release an inode for re-use every time you delete a file, directory, symbolic link, etc. The difficulty is that you determine the total number of inodes in a partition when you format it, and that will never change until you reformat the filesystem.
As I see it, you have four alternatives here.
- See to it that your mail goes to a different filesystem. That would be a different partition on the same disk drive, or some partition on some other disk drive.
- Delete some files on the filesystem in question.
- Investigate whether you're in some sort of loop that's filling your filesystem with files without end.
- Completely reformat the partition. Choose a higher number of inodes. Maybe one inode per 1024-byte block.
If alternative #3 wasn't of use, then alternative #4, painful as it is, will be the most useful in the long run.
Hope this helps.