Sounds like it may be an issue with a 3rd party plugin you have or customization.
I would check a couple of things:
- Do you have any caching plugins installed?
If so, they need to be disabled during an update to ensure you are not being served outdated files once you make the update.
- There may be a plugin conflict with a 3rd party plugin – you can check that by disabling then reactivating a plugin one at a time to see if you find a conflict there.