I think the issue here is that "suspend" has no definition anywhere in the REG. It could be interpreted as you have, essentially negating only one card's ability while the SI is resolving, or it could be interpreted to mean that it stops an ability from acting further.
If it is interpreted as the latter, there would be no issues with the interaction above. Outsiders draws and under decks, SI activates which stops his ability from further acting, so he still keeps the card. Then, Abigail interrupts and under decks, giving outsiders SI. This "suspends" the CoA from finishing until SI is resolves, and i would argue that Outsider's ability wouldn't be removing abigail again because in SI, you must negate the card removing you, and no other abilities can activate during that time.
I may be wrong, and I don't totally understand the finer details of how SI works, so if any one else would like to give input, that would be great.
