This is possibly a hard disk issue, however since you say the hard disk was full a month ago then the issue may be due to lack of space.
You can fine tune recordings and recording space by going to Recordings > View All >
There is a percentage indicator in the top left hand corner so you can see how much HDD space has been used.
Clicking on the top row and selecting Manage Storage > Enter your pin number > brings up a new screen where you can set your default options for deleting recordings
Auto-delete when space needed can be switched to Off or On. This function will automatically delete the oldest content when disk space is required for a new recording. By default, it’ll be off for existing users but for new installs it’ll be on. (This may be why when the 360 gets to around 80% full some recordings fail, possibly depending on the length of the program, and older recordings are deleted)
You can also further fine tune recordings using the Fast Clean-up options in the same section.
If you have more than one main box select the box you wish to perform these actions on
From there you can :- Delete all fully watched programs.
Delete all recordings older than 6 months.
Delete all recordings.
Stop all future recordings.
Delete and stop all recordings.
You can also protect shows and ensure they aren’t auto deleted when auto delete is turned on:
Saved > Recorded > See All Highlight (select) the program by name and click on the edit “pencil” icon on the right side of the bin (delete) icon, then either turn on or off Protect from auto-delete for that program.
If space is required for a new recording, unprotected recordings will be deleted using this logic: Watched, oldest to newest recording. Unwatched, oldest to newest. Content that is being watched at the time will not be deleted. And if all content is protected, the recording will fail indicating this as a reason