I'm not sure if you can possess respect. I think if I had worded it differently, such as 'They were no longer afraid of losing their colleagues' respect' I wouldn't have a problem with the apostrophe, but it just doesn't look right to have an apostrophe indicating possession at the end of a sentence. Thanks!
It's "the respect of their colleagues", without an apostrophe. When you come across a potential plural/possessive confusion, think about what you'd have in the singular, or if the noun were "children".
"They were no longer afraid of losing the respect of their leader."
"They were no longer afraid of losing the respect of their children."
These examples help illustrate that you're using the nominative plural, not the possessive plural. Hence, no apostrophe.