It seems the rumours are true, the government of Zimbabwe is only issuing births and deaths in emergency situations as they say they are facing technical challenges with the normal process of issuing birth certificates and death certificates. The Registrar General’s offices did not explain what the exact technical challenges were, they just confirmed that they were having technical issues.

The Civil Registry Department wishes to inform its valued clients and stakeholders that it is experiencing technical challenges with its system, which has affected the issuance of birth and death certificates.

However, these documents are still being issued manually in emergency cases.

… The ministry of home affairs is working on a permanent solution to these intermittent system challenges
Registar-General Henry Machiri

It is also important to note that the issuance of national identity cards and passports has not been affected by these mysterious circumstances. These days it takes only 5 working days (one week) for you to get your passport and most people say this is a very smooth and mainly pain-free process. The government has also said they are working on clearing the passport backlog from when they were facing technical issues with passports.