When two financial institutions merge, when is the SIPC protection for an individual owning a brokerage account in both places reduced?

The purpose of SIPC protection is to provide a limited guarantee for the retail investor of their cash and securities in the event of a bankruptcy.

From: https://welcome.schwab.com/#:~:text=Schwab%20and%20TD%20Ameritrade%20are,as%20two%20separate%20broker%2Ddealers.

• Schwab and TD Ameritrade are working together to combine the strengths of our firms and merge as one company to benefit you. We expect this to take between 18 and 36 months.
• Until then, Schwab and TD Ameritrade will continue to operate as two separate broker-dealers.

Given that they will be separate legal entities until the customer's accounts are unified, I expect that each will have distinct SIPC registrations.

From: https://www.finra.org/investors/have-problem/your-rights-under-sipc-protection

SIPC’s power to protect customers of former SIPC members ends 180 days after the member loses SEC registration. The SEC normally does not terminate a broker-dealer’s registration if the SEC knows that the broker-dealer owes securities or cash to customers.

So until a customer's accounts are unified, they have 500K USD SIPC at Schwab and 500K USD SIPC at TD Ameritrade. Once everything is moved under Schwab, the single broker-dealer 500K USD SIPC limit applies.