Hi Romina,
This sounds somewhat similar to a problem I've had in *BEAST. For me,
the problem came from over-parameterizing the models of evolution for
each partition. Look at your files in Tracer and see the parameters
that have low (red) ESS values; if some of your nucleotide
substitution parameters for each partition are low (filename.CP#.at
[or .ag, etc.]), there is probably not enough information within each
partition to help the analysis converge. Try keeping your data
partitioned by codon, but giving the partitions a simpler model, like
the HKY model (even if your model testing program told you
otherwise). This changed my ESS values on the posterior and prior
from around 20 to well over 800!
Good luck,
Jared