I have changed the price for a few courses that I have on Udemy, I have pressed save, and pressed the refresh button, and I have looked at the course via incognito, and the course is still not showing the new price, even a few days after.
This course I changed to £74.99 and when I go on the course landing page via incognito, sometimes the course price shows £49.99 and sometimes £69.99.
If you opted into Udemy's Deals program (check at https://www.udemy.com/user/edit-promotional-agreements/) then you've given them permission to adjust your list price. You're probably seeing the system trying to experiment with different prices to learn what students are really willing to pay for your course.
If you want your course to be offered firmly at the price you set, you'll have to opt out of deals. But that will probably do more harm than good.