just done a quick google and cable across this
https://www.horizonmb.com/threads/129112-Tut-How-to-fix-second-monitor-going-black-on-certain-games
not too sure if this will help but also found this post
https://forums.geforce.com/default/...-black-when-playing-game-fullscreen/?offset=7#
I had no issues with my second monitor at home staying on while gaming as I had my hardware monitor software running on it but then I do have a old card (Radeon HD 5830)
I know one is a Nvidia card but it states it was down to the Areo Theme on windows 7 so may be worth trying