I can only run Fortnite 1 day out of 2

Did not worry but thanks for the help it's a microsoft problem ...

Hi. My name is Brilliant, and I am happy to assist you today.

Here are a few troubleshooting tips you can try to resolve your query:
- Restart your device.
- Update Windows.
- Update your device drivers.
- Update the Xbox and Gaming Services apps.
- Sign into the Xbox app and Store using the same account.
- Remove and reinstall Gaming Services.
- Make sure your date and time is correct.
- Disable your antivirus.
- Use the app troubleshooter.
- Repair and reset the Xbox app.

For more details on the above and more troubleshooting tips, kindly visit: https://support.xbox.com/help/games-apps/troubleshooting/troubleshoot-games-windows-10

I hope this helps resolve your query.

But normally including Fortnite it is not necessary. Normally for all other playing must be console started with my account, then my children can switch to their account and everything is OK. I have the only problem with this split screnn feature, that is
why I am trying to understand, if I can use the splitscreen somehow without making the console the home Xbox.

Generally I found the only way how to run Fortnite splitscreen on my console:

1. returned back my home Xbox to my console

2. start Fortnite under occount of one child

3. inside game first log out other players and then log in second child - only in this case possibility to add 2nd player become active.

I did play battlefront 2 for about 6-8 hours yesterday and now it’s happening after playing for only 1-2 hours. But it never happened to me when I played any of the forzas all day for days in a row, even fortnite when I used to play that.

Contacting Epic Games is your best bet. This is ONLY happening to Fortnite so it is a issue with the game and the Devs.

Like you said above it happened 2 days ago ONLY with Fortnite.