Good question, tough to answer. Most hydrangeas do best with no pruning. They then get to grow into huge tree like shrubs as nature intended. Most gardeners do like a more tidy look so every spring you can prune back anything that looks dead, diseased or damaged. There are many types of hydrangeas but I will assume yours are the classic big round balls or mopheads that flower with blue or pink petals. If so, then these older hydrangea macrophyllas only flower on 2 year old wood.  So pruning every year cuts off the old wood that has the flower buds at the tips leaving you with just foliage. You can shorten the branches in spring that already flowered last year, but leave the branches alone that did not bloom. They just need another year to make buds. The sickly hydrangea may be a more tender variety that is killed back each winter from the cold. Or it could have root issues due to poor drainage, big boulders below or even a runway for mice or moles beneath the surface. I suggest you dig it up and move it to a new location.  Then do not prune your large hydrangea this year and I bet you will have plenty of flowers next summer. One more thing - if you live in a cold climate then invest in one of the newer cold tolerant hydrangeas called "Invincibelle " from Proven Winners. Then if a late cold spell hits in the spring, your hydrangeas will not lose their flower buds and your summer will be full of flowers. Keep growing, Marianne Binetti