I also have the idea that money to live on would be a problem. Perhaps anything contracted to Anne (from say, her mother) is too small to be of help or perhaps Sir Walter's very good ability to be a bad father and his living above his means for so many years is at fault.

Chapter 1:

"While Lady Elliot lived, there had been method, moderation, and economy, which had just kept him within his income; but with her had died all such rightmindedness, and from that period he had been constantly exceeding it. It had not been possible for him to spend less:"

Chapter 4:

“Troubles soon arose. Sir Walter, on being applied to…professed resolution of doing nothing for his daughter.”

“Captain Wentworth had no fortune. He had been lucky in his profession; but spending freely, what had come freely, had realized nothing.”

“Anne Elliot, with all her claims of birth, beauty, and mind, to throw herself away at nineteen -- involve herself at nineteen in an engagement with a young man, who had nothing but himself to recommend him, and no hopes of attaining affluence but in the chances of a most uncertain profession, and no connexions to secure even his farther rise in that profession.”