I noticed a huge difference in my posture after I installed a backrest on my throne. I don't lean back against it, but I sit/lean back just enough for my lower back to touch it ... to know it's there. It's more of a reference point than an actual support.
Ergonomics are a huge factor in playing the drums, I've rearranged my kit so many times to get everything right. You never want to be reaching for anything or leaning to reach something, keep it all close to you. My remedy for being shorter is I also use longer sticks to reach everything without leaning.
Throne height is another big thing to out watch for, a 1/2" difference can make a world of difference in your energy spent and how you sit. If you notice that you're having balance issues when playing make sure you're not sitting too high or low. I play tons of double kick and developing the slower speed doubles requires a very solid base, so I'm very fussy with my throne.
I make a conscious effort to keep my back very straight and head up when I'm playing. I've been working on it ever since I noticed Buddy Rich and Niel Peart both have quite a shoulder hunch from leaning over on the kit.
Easy fix- Imagine that there's a bolt in the center of your chest and attached to that bolt there's a bunch of balloons that are lifting you upward gently. That's how your posture should be.
Also, think about this- when you play, your body is like a satellite dish; it broadcasts your energy towards the front of the room where the listeners usually are. When you are hunched over that energy does not travel outwards but rather it falls in on itself and creates turbulence. If you are aware of this it's easy to maintain good posture.
If for some reason you are still slouching then it's a good idea to check your throne height. Your Center Of Gravity will play into how high it should be; in my experience shorter players actually sit higher than their taller counterparts. As for me, I sit about as low as the throne will go but have noticed over a period of 20 years my seat has raised up about 1.5 inches.
I'm not sure I fully understand what you're saying. Do you start off sitting ok and then find that you aren't, or do you not sit properly in the first place?
If the former, that's relatively easy to fix, but it won't happen overnight: you need to check your position every few minutes and consciously re-adjust it. Eventually good old muscle-memory will kick in and take over.
If you aren't sitting properly in the first place, that's more difficult because you have to identify what sitting properly actually is. I've said it before and I'll say it again: I swear by sitting on your seatbones - these are the bones you'll find if you have a little feel of your "cheeks". Imagine that they are press-studs that attach to your throne, so that you are balancing on them rather than sitting on any other part of your anatomy, this will improve your posture by putting your body in a more correct alignment. Your core muscles will work in isolation to keep you there (but keep checking, as above) thus freeing up the rest of you to play better
I have a reoccurring problem that a lot of times I don't sit properly and it affects the way I play. I move the stool, and have the legs marked where they go. I've also changed seats. I've taken notes of how i'm sitting when I do play proper, like how close my knees are to the bass drums and how i'm facing. But all of these don't always work. Does anyone else have an issue like this? If so any helpful suggestions?