Hello again, after http://www.gamesas.com/index.php?/topic/1116797-duke-patricks-combat-archery-thread-3/page__view__findpost__p__16421960, I've played and tried to troubleshoot the issue I'm having, but I fear I'm getting nowhere.
What I've been doing is I've been disabling mods and then trying to replicate the issue to decide if the ones I disabled are causing it, but this is very hard because the problem's I'm having appears randomly and usually during combat (where things are not easy to notice). The main issue is that I can never say for sure that the problem did not appear because of the last mod I disabled, or because I was just lucky. So I end up disabling a bunch of mods, loading a save game that is right before a battle, playing it 3-4 times to see if any of the issues will appear, and if they still do, I select another bunch of mods to disable and try again. I haven't managed to even get close to finding a suspect.

Scripts I've tried disabling include Fransesco's, MMM (and both at the same time), LAME, Alchemy Advanced, Super Hotkeys and Deadly Reflex. Those were the initial mods I suspected of causing conflicts. I couldn't definitelly track it to them. I'm still in the process of disabling the rest of my mods and trying, but what is left it mostly bells and whistles stuff (such as weather effects and natural environments) which I can't see how they would affect Combat Archery.
I have also tried with OBSE 0019 but it didn't make any difference (but I didn't get any other bugs either, in case you're interested). I am however wondering if the fact that I'm using the Steam version of Oblivion (and obse) might have anything to do with it.
I've also tried using merged patches and whatnot in Wrye's to no avail. At the moment, Combar Archery is the previous to last mod I'm using, only followed by streamline.
A thing I have noticed after many attempts, is that there seem to be 3 groups of scripts that are failing, but they do not fail at the same time. The first group includes the script which drops your extra arrows if they are over the quiver limit and the script that prevents you from picking arrows out of your arrow case after opening it up from the inventory. How I usually notice that this group is failing, is that I will draw my bow while having more than 20 arrows in my quiver (say from the bound bow & arrow spell), and the arrows will not drop. I will know then that it is failing. To double check, I will open my inventory, open my arrow case, put some arrows in, close it, open the arrow case from the inventory again, and see the arrows that I put still there. Dropping the case and opening it from the ground, will not show those arrows inside, but only the ones I had in, before the script failed. I.e. it looks like whatever script is tranferring the arrows from the inventory-arrow-case to the ground-arrow-case, is not working anymore. So this is one group as these two scripts always fail together. This happens more often (usually, after the first time my extra arrows drop from the quiver, the scripts will stop working) but of course, when I try to troubleshoot, I will drop the quiver 10 times and it won't ever fail
The second group is the one I mentioned, where notching an arrow will no longer shake the bow for a bit, and you cannot unnotch the arrow by looking downwards (Other times, instead of not shaking at all, your target will continue moving in one direction as if you are moving the mouse). The bowstring sound will also stop playing and you fatigue will no longer drain while holding an arrow notched. All of these scripts fail together, which is why I consider them group 2. This is much more difficult to replicate. I will never go a whole game session without this happening, but it might work for one hour before it stops working. I have no idea what is causing it as it just seems to stop working at random times, after I've just fired an arrow. It's not easy to notice either (I usually notice that my notching is not shaking any more) so when I do realize the scripts have stopped working, I can't figure out with what it correlates to (I don't have any leads). I can continue playing after this has happened, but of course it removes some of the drawbacks of combat archery and I find it unfair.
The last group is the scripts relating to backward movement. This fails rarely as well, but I will usually notice that my speed is stuck at -30 or something and I'm not falling down or stumbling anymore when moving backwards. I can use the unofficial oblivion patch in-game item to reset my attributes so this is easier to work around.
So that is all the effects I've noticed. By restarting the game, all the scripts will start working once more, so usually I do this when all three groups have failed. I present all the investigation I've done here as thoroughly as possible and ask if you can point me in some direction I can investigate more fruitfully. I don't know if there's some kind of debug mode or anything that I can use to track this down as I'm mostly a user and not really familiar with the tools.
I hope I've provided some useful info as I honestly don't know what to do.
Cheers!