Quite the contrary, due to the high demand, rents are on a steady rise. [1]
The government is issuing caps now on how much higher the rent can be with new contracts (there are already caps for how much rent can be increased with an existing contract, but when old tenants move out, they could ask for any price on the new contract, especially when renovating the place - which led to shady methods to get long-term tenants out)
[1] http://www.wohnungsboerse.net/mietspiegel-Berlin/2825