It was a subject, however, in which she often indulged with her fair friend, from whom she received every possible encouragement to continue to think of him; and his impression on her fancy was not suffered therefore to weaken.
Ok, so this is early 19th century language. Today, we would say: the fact he liked her (impression on her fancy) therefore was not allowed to (today: did not) weaken.
The old meaning of suffer was allow or permit.
Perhaps best known to English speakers from the Bible phrase: Suffer the little children to come unto me....[Mathew 19:4]
Today, fancy, the verb, is still used a lot in BrE: Do you fancy a drink? AmE: Would you like to have a drink. Also, for example: "He fancies her." That means "He likes her." in the sense of:he wants to date her or go out with her.
The noun is less used today but was very much in use in the 19th century to mean. In the passage, therefore, her fancy means: her liking him or her fondness for him.
Samuel Johnson's dictionary of 1828 has imagination for fancy, of course, but it also means: fondness, liking, caprice, humor, and others, all of which stand in contrast to reason. In other words, a fancy is something that does not derive from reason; it may arise in the imagination but the word cannot be reduced to the word imagination only. The dictionary was published some 30 years after the novel cited in the question. So the definition is relevant.
A Dictionary of the English Language, Vol. I