Question: I am early in this design but am imagining a fictional world in the age of exploration including classic fantasy tropes of monsters and magic, with renaissance era technology, that is cannons, muskets, clockwork and wacky renaissance war machines perhaps entwined with magic albeit to limited effect or making use of fantastical beasts. I would like the world to stay in this state of technology for as long as possible.

So I indeed ask, What would stop advancements in technology beyond this state? Specifically weaponry?

Answer: 
Religion or culture
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We can see both Religion and culture reject many advancements in the fields of science. Look at astronomy or biology with Religion for example. Though there were advancements, many advancements were rejected by the church in medieval Europe. The advancements were discredited and the people who made the discoveries put to death or incarcerated. It wasn’t that there wasn't progress, but much was made difficult.

Culture as well. Look at the Amish for example. But in a greater scale you can look at the whole of the USA. Advancements in trains or social norms in gun control are rejected because of their culture. They view that they have certain rights for their guns. They view their cars as essential as the indoctrination of the people did it's work, making any alternative unthinkable now that the whole infrastructure is setup to support only cars.

Human complacency with the current world is all you need. They obviously know the world is flat, they are the center of their world and nothing is going to change that. Anyone thinking differently or having proof can easily be rejected, preferably by hurning them.
Empire
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The combination of this technology and of magic let someone unite the region. He suppressed war with a heavy hand and discouraged other innovation as causing unemployment.

Central control gave innovation no place to hide, and the emperor did not fear a rival empire would take it if he didn't.