Disk is running out of space on K2 server.
The only thing to check from purely K2 side is your logging settings. There are different types of logging in K2 (host server, ADUM and SmartObjects) and the logging detalization level for all log types can be increased for troubleshooting purposes.
General recommendation is to avoid use of detailed logging outside of the cases when you troubleshoot specific issue. Once troubleshhoting is completed you have to revert to default logging level. This is especially try for SmO log files which do not have any settings to limit size of output files and normally quite voluminous - these logs should be enabled only for troubleshhoting purposes and disabled completely as soon as you finish your troubleshhoting activities.
There is an existing feature request to add configurable file size limit option for SmO logging. HostServer logs and ADUM logs also can produce high volume of logging (especially if you raised logging lever and/or there are some issues in environment) but at least log files are split in separate files with configurable file size limit.
Please refer to the following documentation for K2 logging to reduce the logging level:
Check if space was consumed by K2 logs and remove/archive old log files. Make sure that you do not run unnecessary logging and logging levels are not raised above default values recommended for normal operations.
Note that any changes of K2 logging configuration require K2 service restart to apply them.
Refer to the following KB for details: http://help.k2.com/kb000298.