A related issue was discussed in this thread:
Where starting in October-ish, launch groups would randomly include several instances where they say a client is running, but nothing for it would show, and it could not be closed or re-launced via the EVE launcher. It was somewhat tricky originally to find and close the ‘stuck’ client (using Task Manager).
Then there was a period of about 3 weeks (for me) from approx. late Nov. to early Dec., where none of the clients I launched (I launch in groups of 5, 4 or 3 accounts) got stuck. Then for the past 3-4 weeks, I’m back to getting stuck clients again, but now the launcher has been adjusted so you can just click on the “Client is running” flag in the EVE launcher and it will shut the stuck client down, and you can re-launch.
So it’s possible CCP is attempting various things with the launcher but it isn’t ‘fixed’ yet. Or of course it’s possible CCP isn’t even aware of the issues they’re creating with various changes to the launcher. Hopefully it stabilizes soon.