BEAST is a method for sampling all trees that have a reasonable
probability given the data. One of the assumptions underlying the
BEAST program is that there is a binary tree that has generated the
data. Just because (for example) three taxa have identical sequences
doesn't mean that they are equally closely related in the true tree -
it just means that there were no mutations (in the sampled part of the
genome) down the ancestral history of those three taxa. In this case,
BEAST would sample all three trees with equal probability ((A,B),C),
(A,(B,C)), ((A,C),B).
This is what is happening in your analysis, with the identical
sequences. Because you are summarizing the BEAST output as a single
tree (presumably using TreeAnnotator which picks a specific tree from
the trace that is representative and annotates it with posterior
probabilities of clades) you will see some particular resolution of
the identical sequences, based on the selected representative tree.
But the posterior probability for that particular resolution will
probably be low, since many other resolutions have also been sampled
in the chain.
One of the results of the way that BEAST analyzes the data is that you
get an estimate of how closely related these sequences are, even if
the sequences are identical. This is possible because BEAST is
essentially determining how old the common ancestor of these sequences
could be given that no mutations were observed in the ancestral
history of the identical sequences, and given the estimated
substitution rate and sequence length.
So in general: you should ignore *all* splits in the consensus tree
that have low support. In terms of the identical sequences, the only
node with the possibility of significant support would be the common
ancestor of the identical sequences. If this is the case then you can
confidently report the age of this node, but should not try to make
any statements about relationships or divergence times within the
group of identical sequences.
I hope this helps.
Cheers
Alexei