uuum...think i found the problem maybe, when you start the game it will wont automatically go to the 'new' account but the other account you created. Why is this important? For some reason when you play singleplayer when even loged in (for the first time) to your 'true' account ,e.g. mine being 'shadow999999', it will instead save the save data to the 'new' account instead of the correct acount but after the second time (when your data apears lost) when then you save it will apear in that acount. I'v only tried this twice so i dont know if it switches the acount around each time but if you have an extra acound and do/do not have the 'new' account in the profiles part of confiqure then youll have to search for it in either steam directory or your documents directory.

edit: sorry if i seem vage about what im saying here but to sum it up just look for your saves in, for me it was, the documents which one will be called arma 3 and the other being called arma3 - other profiles which is where the saves are kept.