I have a category that each morning around 8:15am or so I have to go in and make it active. Our store is tied into a ERP system called OpenERP so don't know if the syncing process is causing issue.
My First guess would be this - do you have any integrations with other systems that could be changing this setting. Sounds like yes and you know where to look. Search in the code for changes to category->isActive or ask your developers to do this.
I guess must be you have set CRON job for the same. Take a help of developer and make script to set its status as you want. Cheers