Sorry to necro this one, but it comes up as my top result for a Google search on the topic, and I ran across a cause for this, and a fix, that might apply for many people experiencing it.
I had the same scenario as OP: liaison on site, but mayor stuck in his office in "Conduct Meeting" mode but never completing the meeting and so unable to meet with the liaison.
As someone else noted, this was happening because the meeting delegate was a dwarf that could not get to the mayor's office for the meeting. But unlike that situation, "Attend Meeting" didn't show up in the unit screen to allow me to find that delegate, because he was Chained up in jail. And like many small forts, the mayor was also the sheriff... being stuck in Conduct Meeting was also preventing him from releasing the chained dwarf that he was supposed to be meeting with.
I noticed this only at random. Removing the mayor as sheriff and appointing another dwarf did not cause the prisoner to be released, even though his sentence was up. I had to deconstruct the chain, whereupon they promptly met and the mayor was freed up to meet the liaison immediately after.
So--this could be a common issue in forts where the mayor is also the sheriff, particularly since ending up in jail is a sure path to many unhappy meeting requests.
On the plus side, I got zero annoying mandates while the mayor was stuck, so I soon regretted freeing him up again.