Title says it all.

If you lose an intrigue challenge is it possible for Knight of the Rainwood to be randomly discarded?

Thanks in advance for the answer!

Yes, because his ability says that he can't be discarded from play. He is not in play while he is in your hand.

Even if it didn't say "cannot be discarded from play" and simply said "cannot be discarded" instead, it still could be discarded from your hand or deck.

All card text is only active while it is in play unless it specifically says otherwise. (Although, to be fair, "specifically" often has to do with the mechanic rather than the words "from your hand." For example, event cards do not say "from your hand," but the mere fact that they are event cards means they only work from your hand. Similarly, the text on something like Edmure's Host, saying to lower the cost to play it based on the traits of other cards in play, lets the "to play" mechanic specify the "from your hand" bit instead of specifically using the words.)

Thanks to you both!

That would indeed make sense, hadn't thought of it that way