I found a workaround. It depends on your ability to keep history on the browser but here is goes.
1. Use the browser you always you. DO NOT clear history.
2. New tab open
https://portal-portail.apps.cic.gc.ca/ and finish the log in process. You will now see no data but you are logged in.
3. Now open a new tab and type
https://portal-portail.apps.cic.gc.ca/home/application-status/
4. If history is your friend you will see something of a number pop on the URL. eg.
https://portal-portail.apps.cic.gc.ca/home/application-status/123456?lang=en
5. If you are in luck you would be directly on the details page of the application.
Edit -
5a. You may need to click on your profile or any other link at least once to "prime" the website. Seems to only work if you have clicked on at least one link inside the portal before pasting the application-status URL on the same tab or a new one. I would also suggest incognito mode to avoid any old caching data causing issues. Once you find that URL protect save store somewhere else before playing around as it will work but once you lose that number there is no way to "figure" it out.
I just did that and I could use it successfully on Chrome. I actually found the link on Safari as that is my default browser but it won't share the session between tabs. But if I log into one tab on Chrome and use the deep-link on another browser I am in. This might be handy for people who got email but are stuck not being able to access the messages.