Couple of things:
1/ If and when a player rejects you can re-offer if you wish. Save the Inbox message sent to you because that has a re-offer link in it. The negotiation link will disappear from the draft page so the message link is critical if you want to re-offer.
2/ Once you have offered demand, never retracted it, and the player has rejected outright, you are in line for a Type D pick next season.
3/ If you really want the player and not the Type D, you can re-offer multiple times. One time I eventually got a player I really wanted on about the fifth or sixth offer.
4/ tlowster's right, you can't get a Type D for a player who was drafted with a comp pick.