I think the command /mcscoreboard keep should be added to mcmmo. I know the command comes with a stock version of mcmmo and the command keeps /mcstats open untill you type another command to make it go away or if you relog. I only suggest this cause I enjoy seeing my stats all the time, it helps really in no way at all but its a nice perk.
I've played a fair bit of mcmmo servers, and from what I've experienced, I think there is only one way to make it stay, and that would be to break mcmmo from 'gaining experience'. I'm not completely sure though, so please correct me if I am wrong. Although, even if this was possible, it would probably lag the server a lot more then it already is. To have mc stats loading constantly would be like running a mod. It would lag, especially for the scoreboard(since that is numerous people updating info at once). Not sure though :P hope I helped. ~Gizz.
You do know mcmmo is already running constantly and this is already a part of mcmmo so no it wont require you to "Break" mcmmo.
In order to keep the mcmmo charts up, stuck on your screen, I'm pretty sure the only way is to stop that skill from gaining experience, then do /(insert skill here). As I said, I've played a ton of mcmmo servers but I've only witnessed this happen then the skill doesn't gain xp. Not sure if it can be put there permenantly or not.