It is something that can be a problem. There are ways to mitigate this, but they’re fairly opaque unless you really know the systems.
First off comets suck. There is nothing you can do about them. Curse the sky and move on.
So one thing to know is that it costs much more to go from +1 to +2 stability than from 0 to +1. Same for +2 to +3. Generally speaking being at +1 should be your target. Admin points are extremely valuable, so wasting them on the stability tax isn’t always a great idea.
So how do you mitigate stability loss? One keep religious unity high. There is a really nasty event called ‘time of troubles’ that occurs if you have low religious unity. It can destroy you. If you get it put all your focus on bringing religious unity up. the game doesn’t tell you this clearly, and it’s hard to find the triggers, but if you get caught in this, it’s a snowball to -3 stability guaranteed. Spin off multiple non-state religion provinces, if need be, into a vassal state. Better to turn 3 provinces into a vassal than lose your country to war.
That’s only one thing, and something most likely during the protestant reformation, so what of all the other losses? One good way is to fill out the Diplomatic idea group. At the end of the group you get a bonus that reduces the stability cost for many decisions. In some cases, breaking royal ties for example, instead of costing prestige and -1 stability it would only cost the prestige. Very useful. It also helps remove the stability cost for some events. This alone is a huge boost.
Another thing is some decisions come with the choice of -1 stability or some loss of tax revenue, discipline, or other such modifier. It is almost always preferable (though occasionally not) to take the other option than -1 stability.
Filling out the idea groups also adds more events to the list of options. Simply by adding more events, certain ones are less likely to occur. Think of it like a lottery, there are X number of balls, and when it decides to draw one you get the result. By making the number X+10 any individual negative event is less likely. Since the basic events tend to have more -1 stability than the idea group events this helps dilute, and reduce the odds of, those coming up.
In particular religious is a good group because it adds several +1 stability events. Note you only have to have the idea group picked, not finished, to get most events. Economics has one, administrative as well. Several of the military ones have negative stability events, but they are usually a choice where you can opt for some reduction in military instead. Just know that the more positive your stability is, the more likely generic events are that give you negative stability.
So basically just stay around 0 or +1, unless an event bumps you up. Diplomatic and religious groups help a lot, though administrative is useful too. More idea groups is better, as it improves your odds.
I can understand why you get frustrated Tom, it can be annoying for sure. At the same hand it’s one of the mechanics that provides the most push back against player expansion. It throws a wrench into those well greased gears I’m turning, and if I’m not paying attention to internal affairs at the time it can really be disruptive. In time it does become another tool in an experienced players belt, and a way to disrupt your enemies.
EDIT TO REPLY TO REZAF:
Coalitions are interesting. I’ve poked around the Paradox forums, so I know why some people hate the mechanics, I just happen to disagree. Yes once you get a certain size you can just bounce around different regions so that, say, Russia and Lithuania coalition you, you move to your west and beat up France and Spain. By the time you move east again Russia has left the coalition, etc. Honestly though once a player becomes that powerful there isn’t many meaningful ways to truly threaten that player. They’ve won, and are just painting the map now. It does make you be more careful in the early game though, and I like the decisions it forces at that point.