The question is, when you add the license back after it's lost then close MC and run Stacer again, does it lose the license again? If so, Stacer is probably removing something vital for MC to stay registered. JRiver probably won't go into specifics on what file(s) could be involved and where they're located, as that could cause them issues (so not going further with that). If I had to guess, if Stacer is directly causing it they'll probably recommend to not just not use Stacer on Linux boxes running MC.
Now, if running Stacer isn't causing the license to be immediately lost, there are other things that can cause the registration to be lost like changing hostname, MAC address randomization, system clock is incorrect, etc.