Can a single copy of a character with SIDELINE ACTIVE keep going back into the sideline and coming back out once it has been KO'd

For example SIDELINE ACTIVE character comes onto the map once a shared keyword character gets KO'd. The SIDELINE ACTIVE character is then KO'd. Can the SIDELINE ACTIVE character then go back to the sideline to be brought out again once another shared keyword character is KO'd?

I don't think so. My understanding is the KO pool is separate from the sideline, so once dead you can't come back unless another figure allows it.

This is correct. Just look at XMRF 008 Sentinel to see a situation like OP was asking about that is specifically spelled out:

"RETURN FOR REPAIRS: When Sentinel is KO'd, instead of putting it in your KO area, turn them to their starting line and add them to your Sideline. (They are still scored.)"

The only exception is when you have a single version of that character on your force and that is the only version you have, then you're allowed to move it from the K.O. "pile" to the sideline. The Foot Clan ninja have a similar mechanic

I wonder what would happen if start with 8 on your force and 7 die.... but max limit is 6 on the sideline?