It's most likely a hardware issue.
I mean that or you will need to clean it more intensively, or you will need to get a new one. Because it is most likely due to the mouse wheel sensors being dirty, or simply "tired".
The good point is that Logitech has an excellent support. I recommend you to contact them, to explain the issue. I have a very good experience of their support, they offered in the past to replace my mx1000 which had a malfunction. (They also send you feet for free, you only have to ask the support for this).
The link to the support is here. However, it seems that their mail support is currently being moved, and is unavailable until the 21st of september. You can still call them, though.
Edit: Ok, "tired" was a bit too fast, I couldn't find the word I was looking for. I didn't really mean that sensors are tired, rather that mechanical/physical parts could be, for example in the way the mouse wheel is "held". It could be that the "steps" which are originally on the wheel, are not holding correctly, and any move is turning it, even a bit. It could also be that sensors have a problem, and are simply misplaced or too sensitive.
I suggested more intensive cleaning, but I doubt it will be enough. To me, it's likely that you will have to get a new one (sent by Logitech support or not). But it's not something you can really fix by changing drivers or else.
The only thing which you can do, on software side, is to deactivate actions from the mouse wheel so that it won't bother you anymore (I believe this can be done using AutoHotkey, more details on that if this solution interests you). Though of course you would have to do without a mouse wheel, which is quite disturbing.