If you are repeatedly prompted to log in while using pixiv, please check the following.
1. Are you using private mode (incognito mode)?
When browsing in private mode, cookies are deleted whenever you close a tab or restart your browser, which automatically logs you out.
If you see a screen like the one shown below, it means private mode is enabled, and you will need to log in each time.
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i Private mode on iOS Safari
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Incognito mode on Google Chrome
2. If you are not using private mode (incognito mode)...
If you are not in private mode but are still being prompted to log in, try clearing your browser's cache and cookies. Then, log in again.
*You may also be prompted to log in again if there has been no activity for a certain period or depending on your browsing environment.