What is the lifetime of the synapse in the mature brain?
In adult mouse cortex, synaptic spines can last anywhere from days to months.

I'm not sure that any such work has been done on human Broca's area, but keep in mind that many synapses are experience dependent.  One study found that fear conditioning and fear extinction lead, respectively, to synapse formation and elimination.  So the lifetime of a synapse could depend largely on environmental conditions.