It seems there is some process running at that time and initiating a kill command(may be from DBA side, checking long running process or may be due to blocking), I would suggest you to download famous procedure sp_whoisactive from Mr. Adam Machanic and schedule the same before your Databaseintegrity check triggers and capture the output into a user table, execute the same for multiple times so that you would be able to get all the running session during that interval. You can refer this article on how to capture the output into a table.
Above will help you in finding out the culprit process and you can act accordingly.
There are few questions similar to yours, kindly refer them:
how to check who has killed the job which was running ?if logs are not generated
Please let us know if above helped.
Removed why part of checkdb database from my answer.