Communicaiton within relationships

I used to think that communication was the key for a relationship to work well and last long. Now, I still do believe that it is important but how do you make a relationship work when one person tries to communicate about problems, concerns, or issues and the other person just doesnt say anything at all, but completely ignores you; hopeing that the situation would just soon blow over. I've seen it in romance movies plenty of times but you can never really see the real consequences that it has within the relationship. I wonder if ending the relationship or simply not pushing someone to work on forming a better relationship with you is the better solution. Whether that be a spouse-spouse relationship, friend-friend, co-worker-co-worker, or even family relationships.