You should be OK now, however.

If 6.0.3 is loading, then all is well finally.

I didn't start up SoftRAID after the restart

Run the terminal.app. Paste these two commands in and restart.

sudo kmutil clear-staging

followed by:

sudo kextcache -i /

Restart

Then paste this command into terminal.app:

sudo kextstat -b com.softraid.driver.SoftRAID

Let me know if the output is 6.0.1.52 or 6.0.3.

This tells me your extensions cache is not updating. When the rebuild is complete, attach a SoftRAID tech support file here, and I can take a look.

SoftRAID does require me to update the driver each time I reboot it though.  Is this normal?

Using your video "SoftRAID Replace Drive in RAID" I certified the disk, then initialized it with no problems.  When I first attempted to add the disk, it gave me an error, so I restarted the computer and then was able to add the disk.  However, unlike in the video, I got no info saying the RAID volume was rebuilding.

Is there something else I need to do to start the rebuilding process?  I'm currently on the Free Trial.  

Do I need to pay for the upgrade before the volume will rebuild?

Certify: writes patterns and reads it back.

Verify: a simple read of the raw disk

Validate: reads the data in the volume to ensure it is readable. If all disks are available in a RAID or Mirror volume, it also updates parity data.

So there is no need to really do anything until you add the disk back and rebuild it. As long as the volume is mounting normally, all will be OK. Do not add a disk if the volume is not mountable.

-- I'll backup again (to a different drive) once I pull the bad drive.  Should I run validate on the RAID after I pull the drive and before backing it up?

I assume once I put the new drive in, I'll need to certify, initialize, and add the new disk back to RAID