Aside from keeping someone signed in and the system powered up, there is no way for this to keep running when the user has signed out if you are using the Personal Mode gateway.
As detailed in FAQs below
https://docs.microsoft.com/en-us/power-bi/connect-data/service-gateway-personal-mode
Though one workaround I saw used at a former company, they ended up finding a PC that's usually online and made a new account with a Power BI license to keep it signed in and powered up so the Personal Mode gateway was always operational, essentially making the account a "Personal Gateway Server Account"
Not the best solution and an on-prem is better, but if you are stuck using Personal mode gateway due to corporate policies or restrictions, then you need to be a bit creative sometimes 😂
Please note - I am not affiliated with Microsoft, I'm just an end user like yourself.
Just a regular guy doin' Data Science.
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