Hello bg594,
Thank you for using the Apple Support Communities. It sounds like you're able to sign in to iCloud for Windows, but you find you need to sign back in shortly after. Is that right?
Do you have any security software running on your PC?
A good starting point is with this resource, titled Get help using iCloud for Windows. As mentioned within the resource, first make sure your Windows software is updated. Then, check for iCloud for Windows updates:
To check for updates to iCloud for Windows, open Apple Software Update on your PC. Apple Software Update checks for updates automatically after you open it, and you can choose which updates you want to install.
You can also download the latest version of iCloud for Windows.
If iCloud for Windows doesn't update in Windows Apple Software Update 2.3, go to Windows Control Panel > Network and Internet > Internet Options. In the Internet Properties dialog, click the Advanced tab. In the Settings section, under Security, make sure that you deselect the “Do not save encrypted pages to disk” checkbox. Try to update iCloud for Windows again."
If the issue persists, you may want to try reinstalling iCloud for Windows with this guide: Set up and use iCloud for Windows
Kind regards.