You're welcome. I hope you see this.
I see a lot of students get to the point you describe then Plataea. Without seeing you ride, I'm guessing you are not always going where the nose of the board is pointing, but often sliding down the fall line - either a lot or a bit. So after you make a turn (swap edges), you might be going across a little, but you're also going down. This will be evident by the line you're leaving in the snow. If it's a thin line going across the slope, I'm wrong. Chances are it's a big washy scrape that goes down as much (or more) than it goes across.
When you're not going where the board is pointing, you don't have a good stable base and balance, so when something like a bump or tricky snow comes along, you fall.
To improve this, do some edging exercises, and really concentrate on making a turn, then absolutely go across the run on a diagonal, really going where the nose of the board is pointing. Point with your front hand and arm where you want to go (across the fall line) and look there with your whole head. Practice in both directions so you are doing it on both edges.
You can even traverse so hard you actually go back up hill a little. It's good edging practice.
You will use your knees & the muscles in your legs and ankles to change how your edge is biting into the snow so you can actively control how much you're traversing across, vs how much you're sliding down the fall line.
Once you get the feeling of going where the snowboard is actually pointing you will feel what I mean and it becomes addictive!
Good luck & Have fun!