I have had this problem too, this last month ever since a series of clean Sierra installs on a new 2016 Macbook Pro. PM Dock icon not working or being replaced by a question mark.
Additionally, when I opened PM, Little Snitch would ask if I want to allow outgoing connections. I said yes, any port, forever. But then later it would ask me again the next time I launched. It turns out over the last few weeks Little Snitch has churned out a dozen different rules allowing the exact same PM access. All became instantly invalid, all say something like:
The application "/private/var/folders/ms/qg8fm99c8xj4ng0059bf9nk00000gn/T/AppTranslocation/02854262-93D0-4F48-8F57-EF4B3178AB85/d/Photo Mechanic 5.app" doesn't exist anymore
The application "/private/var/folders/ms/qg8fm99c8xj4ng0059bf9nk00000gn/T/AppTranslocation/D37E0D14-9D83-43DA-B6D1-0AE6EB042816/d/Photo Mechanic 5.app" doesn't exist anymore
Frankly, this is the first time ive ever heard of "app translocation," but Google says there are other apps similarly affected by this new system security feature in Sierra. The problem is that Sierra considers it un-safe to initially open a new app from a .dmg, the Downloads folder, a DVD, another computer (probly what I did) -- anything except for dragging the app directly into the Applications folder and launching from there. So I dragged a fresh copy of the Photo Mechanic 5.app over from the original .dmg and started it from the Applications folder. And so far so good - the PM icon now remains in the dock, totally functional, even after a computer restart. WOOFHOO.
The above fix is more thorough, but a quick workaround that I also tried was to nest the PM app inside another folder, any name, inside the Applications folder. Same positive results.