Are you using the 1Password desktop app at the same time?
As the screenshot shows above. Suppose you're using 1Password in the browser independently or with the integration feature disabled. It is expected that 1Password in the browser will be locked when you quit the browser.
Happily, if you use the 1Password desktop app at the same time and enable the integration feature, as shown in the screenshot above. 1Password in the browser can share the same auto-lock settings as the desktop app. Therefore, 1Password in the browser will remain unlocked even if you quit the browser, as long as your 1Password desktop app is unlocked in the background.