In patch 1.9, disasters were introduced to replace the earlier random system of bad things happening.
Now you can see exactly what conditions in your nations raise the progress to a disaster happening to what monthly degree.
For example if you are not in a war and have low manpower, you will get a monthly increase towards a peasant war between +0.5% and +2%.
When you go to war again or raise your manpower, the progress towards the disaster stops increasing, but does not go away.
Is there any way to cancel the progress altogether or at least reduce it again?
Otherwise it seems that sooner or later the disaster is going to happen, because over a long time period you will always have a short period of the disaster conditions being met and this will keep raising the progress slowly but steadily.
Best Answer
The disasters are well documented in the EU4 wiki.
To take your peasants war as an example, here's how it should work:
So, the disaster should go away, if your manpower exceeds 25%. If it has already fired, you need to first defeat all revolts, and have a stability of +1.
Source: http://www.eu4wiki.com/Disasters