Ah, I use the left thumb stick for all movement and a mouse for looking around. If you don't have the thumb stick linked to infantry movement then you shouldn't experience the issue.

Are you using the controller in the game? I can reproduce the issue on two different machines using different controllers.
If the controller is connected but not in use then I doubt the problem will manifest itself.

With the dead zone at maximum the issue happens rarely.
With the dead zone disabled (at minimum) guns will not deploy in prone.
Any dead zone setting less than maximum (10 percent) causes the problem intermittently, becoming more frequent closer to the zero setting.
The issue still exists so please leave the ticket open, thank you

It seems a lot better after the 1.42 hotfix - I think this issue is related to the Y axis deadzone on the controller; I noticed that sometimes the rifle would deploy in prone, sometimes it would twitch as if it was trying to get parallel to the ground. I've increased the deadzone to its maximum value and prone deployment now works first time most of the time.
Changing optics while in prone no longer causes the issue.

Once in prone with the bipod deployed, changing optics mode on a scope also causes the issue to occur, the bipod will fold up and will not re-deploy.

I am still unable to set a modifier key. I've tried setting my controller left trigger in Arma3Profile but that doesn't work. Trying to do it in-game for each specific stance adjust direction doesn't work.

I used to be able to hold the left trigger and use the left thumbstick to adjust my stance.

Edit: it seems like combinations of keys or Mouse & keys can be set in-game by pressing them together but this doesn't seem to work for controller inputs. As I use controller & mouse, this is a problem for me!

Nice big changelog from today's update...but no love for the stance adjust modifier key :(
Still cannot assign a combination of controller keys, triggers or thumbsticks to the stance adjust positions.

Well after today's update to 1.56 there is still no ability to use combinations of controller buttons or controller + mouse. I've again tried modifying Arma3Profile manually, getting the hex values for the controller keys I want to use, converting them to binary as per other key bindings but I must be doing something wrong as I only end up with "+" showing in the stance adjust menu setting :/

...but not today, after the update to 1.50 Stable.

...aaaaand the issue still persists after today's update to 1.48 Stable. One day I hope to be able to Stance Adjust like I used to do :(

...might not be this year, as the issue is still in 1.52 stable...

Issue still persists for me after today's update to 1.44 Stable

Issue still persists for me after today's update to 1.46 Stable

Also created a new profile as advised, issue still exists. Running 1.42 with all DLC.

I have upvoted as well; I use a combo of mouse and gamepad and had the stance adjust modifier on the gamepad trigger. I could then use the gamepad thumbstick to adjust my stance. No longer possible with the new separate key bindings.