In the exact same way that Austen's other titles indicate her novels' central themes, the title Persuasion indicates that Austen's central theme deals with Austen's perspective on a person's ability to be persuaded. In the same way that Austen analyzes the follies and virtues of both pride and prejudice in Pride and Prejudice and the folly of emotionalism, or sensibility, in comparison with the virtue of rational thought, or sense, in Sense and Sensbility, Austen also analyzes both the virtues and vices of either being easily persuaded or being unable to be persuaded.
Austen points out that being easily persuaded is a vice: Anne's heart was broken when she gave in to Lady Russell's advice to not accept Wentworth's proposal because he currently had no fortune.
Austen also points out that refusing to be persuaded is a vice:
1) Louisa nearly died as a consequence of her refusal to be persuaded by Wentworth when he insisted that jumping down the stairs at Lyme was to dangerous.
2) Even though Anne is very intelligent and has a reasonable mind, her family refuses to listen to her advise and be persuaded by her on matters of finance.
3) When Anne meets Captain Benwick she advises him that reading only poetry depicting broken hearts and wretched minds may not be the safest thing for him and suggested he begin reading "our best moralists, such collections of the finest letters, such memoirs of characters of worth and suffering...[that would] rouse and fortify the mind" (Ch. 11).