My understanding is that for a rental property, the added basis must be depreciated over the life of the improvement.
Correct. But land is not depreciated. However, a number of "land improvements" are depreciated. An incomplete list is included in IRS publication 946.
If depreciation is not taken in any tax year then that depreciated amount is lost.
In a sense, yes. But when the error is discovered, it can be corrected by either amending the return, or by filing IRS Form 3115 to correct things. Which you do, depends on the circumstances and time frame.
i.e. if no yearly depreciation is taken then all the basis from the special assessment will be lost at the end of the improvement's life. Is my understanding of this correct?
Somewhat, yes. So if you have a 15 year property and you don't depreciate it while it's in service the full 15 years and sell it, your cost basis on that asset would basically be zero and you'll be taxed on the full sales price of that asset. But do keep in mind that tax rates for both capital gains and depreciation recapture can be anywhere from 0% on up, with a maximum of 25% for recaptured depreciation.
For capital gains, it's my understanding that most people will fall in the 15% range.
