Hi, fellow Tableau for Mac user here...
I don't quite understand the "same user account"...do you mean for Tableau Desktop or Tableau Server/Online?
If you mean for Tableau Desktop I'm not sure how you'd set that up in the first place, do you mean you have separate accounts on your Mac and each is running Tableau? In that case then you're potentially running into how Tableau's licensing system works...we can have two installs of Tableau Desktop and it's possibly treating the three accounts as three installations, though I've never tested that out.
If you mean for Tableau Server or Tableau Online then I'm not quite sure what you mean by "one of my logins gets deactivated"? There are a couple of challenges here that I know of:
a) One is accessing Tableau Server or Online from Tableau Desktop. In this case I've found that when I have multiple instances of Tableau Desktop running at the same time and connect them to different instances of Tableau Server/Online (including different sites within a single Server or Online instance) sooner or later Tableau Desktop can get confused and starts throwing errors. I've found I can leave the multiple instances running but before doing things like publishing or refreshing a Server published data source I have to double-check that I'm connected to the right instance.
b) The other is having a single web browser open while there are multiple tabs or windows connected to different instances of Tableau Server/Online then I can run into similar kinds of problems. For example if tab A is on instance X then I open tab B is on instance Y and then go back to tab A and click on the Projects tab it can jump to the projects for instance Y. My solution for avoiding this is to open up entirely different web browsers (Safari/Chrome/Firefox).