  Massive gas-rich galaxy discs at $z \sim 1-3$ host massive star-forming
clumps with typical baryonic masses in the range $10^7-10^8$~M$_{\odot}$ which
can affect the orbital decay and concurrent growth of supermassive black hole
(BH) pairs. Using a set of high-resolution simulations of isolated clumpy
galaxies hosting a pair of unequal-mass BHs, we study the interaction between
massive clumps and a BH pair at kpc scales, during the early phase of the
orbital decay. We find that both the interaction with massive clumps and the
heating of the cold gas layer of the disc by BH feedback tend to delay
significantly the orbital decay of the secondary, which in many cases is
ejected and then hovers for a whole Gyr around a separation of 1--2 kpc. In the
envelope, dynamical friction is weak and there is no contribution of disc
torques: these lead to the fastest decay once the orbit of the secondary BH has
circularised in the disc midplane. In runs with larger eccentricities the delay
is stronger, although there are some exceptions. We also show that, even in
discs with very sporadic transient clump formation, a strong spiral pattern
affects the decay time-scale for BHs on eccentric orbits. We conclude that,
contrary to previous belief, a gas-rich background is not necessarily conducive
to a fast BH decay and binary formation, which prompts more extensive
investigations aimed at calibrating event-rate forecasts for ongoing and future
gravitational-wave searches, such as with Pulsar Timing Arrays and the future
evolved Laser Interferometer Space Antenna.
