HA!
I think I know what it is: the ML guide on p 16 says in footnote 11: 
"Note that the hierarchy produced by ReComputePreconditioner() can differ 
from that produced by ComputePreconditioner() for non-zero threshold 
values."
So when the matrix changes too much, the const double aggregation_threshold 
in PreconditionAMG::AdditionalData would lead to different matrix entries 
being considered.
That is why it was also working for (constant) Laplace and (almost constant 
Hyper-) Elasticity, but not so well for Navier-Stokes, since I initialized 
the AMG in the first timestep, where convective terms are completely zero 
starting from the quiescent state.
Hope someone finds this in the future and updates their AMG every few 
timesteps as well!
Best
Richard

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