Honeysuckle that fails to bloom has probably been planted in an area where it receives too much shade. Although most honeysuckle varieties tolerate shady garden conditions, they bloom better when they receive at least 6 hours of direct sunlight per day.
Another reason why honeysuckle sometimes fails to bloom is because it has been overfertilized. Too much nitrogen causes lush, luxuriant vegetative growth but inhibits flowering. Honeysuckle rarely requires fertilization to stay healthy. In fact, fertilizing honeysuckle too frequently causes them to fail to bloom as much and can encourage them to become invasive. In some parts of the country, some honeysuckle varieties are considered weeds.
Honeysuckle is very easy to transplant. Honeysuckle can be transplanted during the early spring before the plant breaks dormancy. Be careful of overzealous pruning, however; honeysuckle flower buds develop after the plant has finished blooming for the season. If you cut the plant back during the spring, you remove this season's flowers. Honeysuckle should be pruned immediately after its bloom time has ended in order to promote next year's flower growth. Pruning the honeysuckle tips throughout the growing season can also stimulate new bud growth.
If nothing else works, try rejuvenating the plant by cutting it completely back in the autumn. You may have to wait a year for it to bloom again.