Birnberg said the party had a month-to-month lease on the old headquarters on LaBranch until earlier this summer. At that time, the building was sold to a developer who intends to tear it down for a new project. The owner gave the GOP permission to help with the razing. The Democrats moved into new digs on the North Loop.
I don't see that there's enough information here to decide what happened. It could just as easily be true that the Dumbos didn't want to lease from the new owner and negotiated out of their lease.
The Republican Party email in the above linked thread includes this line: "The building has been sold and is set to be demolished. That’s where we come in. The owner of the building has invited us to help with the leveling of the building."
I am going to accept the line that the owner ended the lease early (that it wasn't a refusal by the Democrats to continue renting).