What model DVR do you have?
If it is quantum, issue affecting scheduled re or dings has a fix that is currently fielding.
Skip/rewind time is configurable from a list of options. Look under DVR settings.
Imagine how much data DVR would need to keep to remember all of the shows you have ever recorded. How long should they remember what shows you watched? Does any DVR remember everything you have watched and never record again?
You can set DVR to record new and reruns without recording 5 copies. Just set series to have duplicates set to no. Will only have one copy of an episode of a show on DVR at a time. But as you have said, will record an episode you have already watched once deleted.