Let's scale up an animal.
If length is $L$, and we don't change the proportions, then the mass of the head+neck will scale as $L^3$. If the neck & head are being held horizontally, the lever arm scales as $L$, so the torque at the base of the neck scales as $L^4$.
The width of the neck scales as $L$, so the force on the tendons/muscles scales as $L^3$. The yield strength of a tendon/muscle scales with its cross-sectional area: $L^2$.
The force is going as $L^3$, but the yield strength is going as $L^2$. My math agrees with your intuition: as you make an animal bigger, eventually the neck won't be able to handle the stress.
The reason why the giraffe can get away with long necks is twofold, I'd guess:
1) They have a proportionally thicker neck. Look at a picture of giraffe. Note that the neck gets extremely thick toward the base along the front-to-back axis (which is the the axis along which they lower their head), while it's slender side-to-side. Of course, this you can only change proportions so far: eventually the animal will be all neck.
2) We've got a lot of overhead with our short human necks. Ferinstance, I can support weights much heavier than my head with my arms, despite my arms being much longer AND a bit thinner than my neck.