Death row inmates although convicted and sentenced to death still can appeal the death sentence a certain amount of times until all the death row inmates appeals have been exhausted.
The courts are backlogged and it can take years for a death row inmate to file an appeal and then even if that appeal is denied they can appeal again.
Most death row inmates are executed within 10 to 15 years but some death row inmates have sat on death row for up to 40 years and most death row inmates die of natural causes while sitting on death row before they even get an execution date.