Please help us help you and fill where relevant:
Your LimeSurvey version: Version 3.27.9+210726
Own server or LimeSurvey hosting: Own server
Survey theme/template: Fruity
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I have an active survey which my participants are unable to access. When they try to open the link I provided, they receive a message saying "403 Forbidden. Request forbidden by administrator rules". Yesterday the site worked without issues, but today almost nobody has been able access it.

Can anyone suggest any reasons for this problem?

I can't find that error string anywhere in LimeSurvey. What has changed in the server environment?

This sounds like a server configuration to me. I don't think that Limesurvey can cause that. You should talk to your server admin.

Version 3.27.9+210726

And given the "ancient" version you are running, it is save to say that this didn't happen after an update of Limesurvey. So there must have been some modification to the server evironment.

Independelty of this issue, you should really consider to update your Limesurvey installation. It has not received any updates, bug fixes and security patches since 26.07.2021, which means 1,5 years without updates.