Are you using any extra caching outside of Kentico? I've seen this before when there was web accelerator above the Kentico and we always had conflicts between it's vs. Kentico caching. I'd recommend to use Kentico cache only.
Live pages might not refresh if cache dependencies are not setup or they are incorrect.
Kentico admin has all needed cache dependencies setup, so it should show latest version all the time unless there is caching outside of Kentico layer. If there is no extra caching - try to restart Kentico.
If that didn't help, try enabling Debug for caching (not recommended in production!) and see what sits in your cache and if system updates cached items as expected.