Is the VA Claims Status database updated in real time? If not, what is the update schedule?

If by "Real Time", you're thinking of a system like UPS or Amazon where it's scanned at each step of the way, then no. It could be classified as a more "on demand" type of update system.

It is updated every time the status of your claim has a significant update such or a change in the overall status (i.e., Received, Closed, Ready to Work, etc.). The statuses are inputted manually by the claims processor as they work through your claim.

There is also a difference between the claim information that you see on eBenefits and the claim status information that is within the internal VA system (not different in status, but difference in fidelity).
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* https://www.knowva.ebenefits.va.gov/system/templates/selfservice/va_ssnew/help/customer/locale/en-US/portal/ [login to see] 01018/content/ [login to see] 06605/What-type-of-claim-status-information-will-be-available-on-eBenefits
* https://www.knowva.ebenefits.va.gov/system/templates/selfservice/va_ssnew/help/customer/locale/en-US/portal/ [login to see] 01018/content/ [login to see] 36576/Appendix-D-Index-of-Claim-Stage-Indicators