When I first launched Bixby Developer Studio, it greeted me with a startup screen with a Login button. I clicked on it and it opened a login page in my browser. I logged in that page using my Samsung developer account. The login was successful and a pop-up appeared asking me if I will allow the page to launch Developer Studio (which was already open at that point). I allowed it, but nothing happened; Developer Studio was still showing the startup screen.
I restarted the application but it again showed me that startup screen with the login button. If I click on the login button, it will just take me again to the login page in the browser. And then nothing would happen if I login again.
There are a couple of points you could work on here -
In this case, I suggest you to keep the browser open in the background while clicking on the login button. I was facing the same issue and somehow it worked for me like this. This has been an issue on a Windows machine. On a Mac this problem is not faced till now.
You could restart the Bixby studio itself for logging in again.
Also, I suggest removing the browser cookies as told by shahnawaz above.
Do let us know if this still persists !