First test each drive individually by connecting it directly to the USB port without using the powered hub.
Will each drive connect?
If yes, and you have problems when you use a USB hub, then the issue is with the USB hub firmware. Try another brand.
For the past few years, I have been using a cheap Dynex 4 port powered hub from Best Buy and it will handle 4 hard drives simultaneously when I test with an AirPort Extreme or Time Capsule.
Thanks for your reply, Bob.
I ejected the second drive, in order to get to the third, and when I did, the TC went offline for a minute and then came back on recognizing all the drives. So it looks like everything's good in that respect.
However, I did come to the realization that Time Machine won't back up the external drives when they're connected to the TC instead of my MBP or iMac. So even though it's all working now, I'm not sure whether it's the best set up.
Is there a good backup method you use for this situation?
However, I did come to the realization that Time Machine won't back up the external drives when they're connected to the TC instead of my MBP or iMac
That is correct. The Time Capsule drive and any drives that are connected to the Time Capsule USB port are network drives. Time Machine cannot backup a network drive......it can only back up a Mac and a drive that is connected directly to a Mac.
If you want to use Time Machine, you will need to connect the hard drives directly to your Mac and then back up both the Mac and the hard drives to the Time Capsule.
Otherwise, if you need to connect the drives to the Time Capsule, you could use another application like Carbon Copy Cloner or SuperDuper to automatically backup the data on the drives to the Time Capsule drive on a schedule that you set, such as daily at 10 PM.
I tested Carbon Copy Cloner. It refused to do the job because it couldn't/wouldn't preserve owner membership or preserve extended attributes. So I switched to ChronoSync and it warned me about the same issues, but was willing to run the backup syncs anyway. I've had to adjust the sync triggers to just the basic date-modification-only setting, and I've had to severely limit the number of copies archived and the length of time files are kept in the archive before deletion, so that my TC doesn't needlessly fill up; but the bottom line is that ChronoSync will do the job.
Also, I continued to have issues with the Anker powered USB hub, so I got the Dynex hub on your suggestion. So far I haven't had any of the myriad issues I had with the Anker.