In order to resolve this, you would need to go through the re-authorisation process.
There are multiple reasons the prompt could keep appearing:
The browsers cookies history is being cleaned/deleted.
Upon a successful authorisation, a cookie is placed on the machine, within the used browser. However if the browsers cookies and cache, or history is being cleared, this will then reset the authorisation with HMRC's system.
If your IT has a policy set where your browser cookies are deleted after a certain period, you would need to ensure the HMRC cookie is whitelisted to stop this happening.
Changing the web browser used from the last session will also trigger the re-authorisation process.
HMRC's system recognises and keeps a log of which browser, location and PC/Laptop you are connected to the internet from since the last session, and so if any of these change then it will trigger the re-authorisation process
If HMRC were having issues on their side, and their system had fallen over or was taken offline, once their system is back up and running again, they might require a re-authorisation.