Well, I just took the 4Runner back to the dealer for the second time this week. This time, they took pictures of the issue and spoke to the Toyota rep. Apparently, there's already a TSB for this issue whereby they will replace the clips with a different style supposedly fixing the issue.
Although the actual seat cover is not part of the TSB, the dealer said they will also be replacing the cover at no charge. Service is scheduled for this coming week. I'll post back my results after I've had the work done and have driven it for a while to see if it actually fixed the issue.
I suggest that anyone else having this issue take the vehicle to the dealer and start going through the process to get it covered by the TSB.