What is the main downfall of using QPSK rather than DQPSK in fiber optics?
Simply propagating through space, or through a waveguide (like optical fiber), changes the phase of the carrier, according to 

\$\Delta\phi = 2\pi d/\lambda\$

Of course if d is fixed, you can find a way to lock on to and recover the carrier.

But d is not strictly fixed. In an optical fiber, as the temperature varies, the fiber will expand and contract, changing the physical length of the path. At the same time the index of refraction of the glass making up the fiber will also change slightly, which might counteract or enhance the physical effects from expansion and contraction.

Over 1000's of km of fiber these path length change can add up to many many wavelengths even if there's just a few degrees (or even fractional degrees if you talk about underwater installations) of temperature variation. 

Also, in long-distance fiber optic links, you have optical amplifiers spaced every so many km to maintain the signal amplitude. These optical amplifiers are also likely to have an effect on the carrier phase, and that effect is likely to have some thermal dependence.

I should also add that, due to the invention of the optical amplifiers I mentioned, coherent modulation is actually very rare in the real world. It was widely studied in the 1980's due to the factor of two improvement in channel capacity per watt for coherent modulation. But the development of the erbium-doped fiber amplifier (EDFA) made it more economical to simply increase power than to use the more complex coherent modulation and demodulation.