I found a work-around for this very annoying 365-day filter using Google Chrome.  I don't know if this works on a different browser.

1) Login to QB Online. 

2) Go to the screen where you are having this "last 365 days" issue. 

3) Copy and paste the QB online URL link into another Google Chrome tab or window, so that you have more than one QB online windows open at the same time, and the auto 365-day filter day won't be there in the new tab/window. 

As long as you keep using QB Online using the new window/tab, you shouldn't have a problem with the filter.