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: 
**No oil, no progress.**

The modern world is only possible because we have vast reserves of oil and coal underground - courtesy of pines and shrimp which fossilized in prior epochs. Without coal, even if electricity was discovered there would have been no resource energy rich enough to run large scale power plants. Without oil, we could never have progressed further then smoggy powerplants and into the era of personal, horseless, vehicles and trade.

Simply state that there are no oil reserves on your world and limited coal mines and your civilization is then stuck in the renaissance.

On the side of weaponry all I can add is that it wasn't the military that came up with early improvements to guns. It was enthusiast duck hunters in between the wars. The militaries were content with powder loaded muskets and trying to built continually larger cannons for a long time. The idea of getting off more then a single precision shot from a gun was engineered by sports hunters as a way to hit more ducks. So... Remove ducks from your world?
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.