I'd run not walk to the store and get a new backup drive. Assuming your backups are important, spend the money and grab a new drive. Anytime you are having access issues with an older drive, assume it is getting ready to die. Just because the older backups are okay, doesn't mean that the drive is not having issues. What happens is that a drive will start having problems reading/writing the data meaning new backup files may be corrupt. The operating system will make multiple tries to read the drive and doesn't complain until it cannot access the drive. A hard disk is a motor with a spinning platter like a record player and the bearings get worn, the head positioning mechanism gets sloppy.
Just because you drove your new car across the country 10 years ago without problems, doesn't mean that it will make it this time.
Assuming your computer is working okay right now, if you get a new backup drive and backup the computer you should be good to go. You don't normally need older copies of backups and a new drive will do a full backup initially.
Ask yourself, if my computer died would I lose anything of value? Generally speaking that is a Yes. What you need to know and it's hard to find on a Mac is the number of run hours and the output of the SMART diagnostics of the external drive. What is needed is a Mac version of CrystalDiskInfo which runs on a Windows machine. To my knowledge, there are no free programs that read the run hours and SMART diagnostics for MacOS. While I have drives with 40,000 run hours on them I would not trust them with my family photos. I'm cautious and replace at 15,000 hours or the first sign of trouble. 20,000 hours is about the limit for valuable data.
If you have access to a Windows computer, then search and download a free copy of CrystalDiskInfo. Plug your backup drive into the Windows computer and let it analyze the drive. Look for the power on run hours and any indications of an error. If the drive status is not healthy then you need to swap out the drive for a new one.
