Should I be able to run disk utility on my Time Machine Backups?

Been having issues with Time Machine and backup so I ran disk utility on all my drives: iMac drive, iomega external HD and Time Capsule. When I run on Time Capsule I am getting a failure and this message:

Updating boot support partitions for the volume as required.
Unable to mount volume for repair.
Operation failed…

Time Machine says "last backup Nov 25, 2015." Can't figure out what is going on. Does anyone have any suggestions?

TimeMachine is rock solid. I have used it extensively and exclusively since it came out at on many different machines and have never lost any data. Like any backup system, it is only as reliable as the person using it. You need to have multiple disks rotated at regular intervals. Time Capsule is just one Time Machine disk, so don't confuse the two. You need additional Time Machine backups on other disks. Unfortunately all disks fail eventually. If it says that the last back was a certain date then that is what you have.