Rent control in most places means you cannot increase the rent more than x% per year, where x is fairly low. If the rent is decreasing, you are not allowed to put it back to the original level if the difference is larger than x, so you need to do x% per year for several years just to revert to previous levels.

Depending on how they do it and the location for many areas temporary "discounts" do not effect the "base rent" but in many areas discounts are considered altering the "base rent" and would basically permanently ruin any chance of making money on a piece of property. Can't even sell it if you get stuck with a low base rent as normally rent control forces the rate to pass between owner with very few exceptions meaning no one would buy the land off you.