To have a heart that never wavers means that you will not question if you truly love or care about someone. This has to be done or else you could easily blindly "fall in love" with someone. As falling in love is a process, not something that suddenly occurs. While most of this is subconscious, there is still a level of processing that occurs consciously. Subconsciously, much processing goes on as well. Questioning and thinking that goes on the surface. to say someone has a heart that never wavers, is someone who takes things at face value, and disregards anything bad that appears. This would just cause pain in the person.
I think a better way to say this is to say if someone has a sense of loyalty that never wavers. A heart has to go into question, it is a necessity. Loyalty, in the sense of love can't waver, because then love can't be formed. Of course loyalty has to be formed in the first place. This comes from trust, and the formation of love. If loyalty wavers, then love will dissolve. This is because loyalty in the sense of love, have a symbiotic relationship. If you question loyalty, you question love in a negitive sense. You are breaking two things that are needed with each other. If loyalty (earned, honest loyalty) is in place, love and the heart can waver and question to be sure of things in the saftey that something will not break.
Non-wavering hearts do exist, but they are painful to the person who posseses it. They are also incapable of forming true love with someone.