I think CW had shown a renewal of interest in Anne in Ch 9 when he yanked the toddler off Anne's back, in Ch 10 when he got curious about Anne's refusing Charles in marriage, and when he helped her onto her sister's gig. In those chapters, Anne hadn't regained her bloom, not until Ch 12, maybe brought on by the sea.

As for Mr Elliot's appearance in Ch 12, he seemed to be an incentive for CW to consider the possibility he might lose Anne altogether if he ignored her too long. Mr Elliot being there jarred CW into the reality that Anne was still within marrying age (how pretty she was, etc), as did the presence and interest of Captain Benwick in conversing with Anne.

IMHO, up to Ch 12, CW was still upset about his failed relationship with Anne, and the way he dealt with it was denial. By ignoring Anne (oh she's just the resident pianist, oh she's just the spinster, oh here are the happy Musgrove girls I need to spend time with) he was putting the lid on his issues without really resolving them. So then it's no fault of Anne :-)