Since parts of the brain are recycled every few days does that mean that materialistic theories of consciousness don't work?
That was an interesting read, and I saw nothing to support your statement that "brain parts die every few days".
Neural plasticity demands that some synapses degrade as new ones are formed. But there are (an estimated) 100+ trillion synapses (some put it an order of magnitude higher) so, really, a few here and there means little. It's when there is wholesale loss that problems arise.
A strong argument for a materialist theory of consciousness is that as neurons involved with memory die, so does memory. This is evident in the transition that occurs in early childhood allowing for the formation of long term memory as well as the degradation of short-term memory and other brain functions in people with, say, Alzheimers.
Hippocampal Neurogenesis Regulates Forgetting During Adulthood and Infancy Science 9 May 2014