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You seem to be using a caching plugin, which could be responsible for this. I see in the source code the name “Endurance Page Cache”. This could also be provided by your web host, if you can’t find anything under that name. You would have to clear their cache in any case to solve this.
I agree with @threadi that it is a caching issue – I just checked your site, and the border shows for me even though I am not logged in. Your cache plugin likely bypasses the cache for logged in users, so you see the latest CSS changes when you’re logged in, but site viewers will have to wait for the cache to be cleared before they see the CSS updates.
Your cache plugin (or your web host) will likely have an option for clearing the cache, so doing that should help your visitors see the changes more quickly.