Do housing prices ever come down?

No

Prices are a function of supply and demand. For the last 15 years in the US there have been fewer homes built than households created. This has resulted in a huge gap in housing both for purchase and for lease.  Something similar to this happened in the 1920s and 30s, as the cost of construction rose and fewer homes were built, leading to a rise in house prices that was not relieved until the late 1940s when housing construction boomed, and prices finally reduced.  It is likely that we will eventually see prices come down, but only once several issues of financing, both for builders and buyers are addressed to bring down the cost of producing housing.