The term that might describe someone who habitually rejects offers or favors from others is "refusenik."
In the context you're describing, "refusenik" can be applied to someone who consistently says no to offers or favors without any particular reason. It's important to note that while this term can fit, it might carry different connotations based on the listener's familiarity with its historical context.
Another term that could be used, though less specific, is "declinist," which simply means someone who frequently declines offers or invitations. However, this term is not commonly used and might not be immediately understood in casual conversation.