Losing sincerity is worse than losing interest.
You might not be interested in a certain thing, but if you are at it for any reason then you should at least be sincere. Certain things.... like a job, a project, a relationship or an education and even a dream.
Again loyalty is different thing. Loyal person is one who is firm and does not change friendship with or support for a person or an organisation. Sincere person is one who is not pretending or lying; is honest with other person or organisation. Clearly, two different things.