• How do I prevent making the captions go away when inserting the TV rating bug?

There are two issues here. One is that the logo itself is a video edit and may disrupt line 21. The answer above regarding edits applies here as well.

The second issue is that the v-chip data itself could wipe out line 21. It's rare but possible. If so, then your owner's manual should tell you how to set your v-chip encoder to pass existing captions.