Time Machine won't go back to all dates

I go back & forth between 2 locations every 6 months, and have iMacs running El Capitan at each location; each one having a unique name. To synchronize them, I clone the hard drive at one location and then clone that disk to the 2nd iMac's HD. I then change the name of that computer back to its appropriate name and have the Time Machine backups (use 2 disks) adopted by the cloned iMac.

Just noticed that while all the dates are listed when I enter Time Machine, I can only go back to the date when Time Machine drives were connected to the 2nd computer, i.e. Dates show back to May 28, 2017, however, I can't access anything earlier than December 28, 2017, when the last switch was made.

Any suggestions how to fix this, or do I just have to trash those older dates?

Thanks for any help.

Rich