I'm creating this as a placeholder, so we have a bug number to tag the fixes with.
While this issue has been reported earlier, none of the existing tracker entries refers exclusively to it (instead, they do report it as side effects of other issues that may or may not have been fixed already) - and thus none of those entries is an appropriate reference.
This issue is about damage helpers that are not referenced by an existing crop (i.e. there are no crops that have them specified in the myDamageHelperRef variables on their WorkshopObjectScripts). These invalid helpers may persist in the game and are indicated in workshop mode as crops in places where there are no crops anymore (hence termed 'invisible crops').
There several occurrences of invalid helpers in the game:
(1) When a crop is stored in the workbench, the world model of the crop is removed and its markers (furniture markers and the damage helper) are supposed to be deleted. However, the vanilla WorkshopObjectScript did not unlink the helper from the crop before deleting it, so it remained persistent and was never actually deleted. This issue has been fixed in UFO4P 1.0.5, but any improperly deleted markers created before this fix was installed were still remaining in the game (in other words: that fix was not retroactive).
(2) User reports suggested that some pre-placed crops have duplicate damage hlpers (this has been confirmed in the meantime). When the crop is deleted with UFO4P 1.0.5 installed, the valid marker is now properly removed, but the invalid (duplicated) marker still stays behind because its reference is not known to the workshop scripts.
(3) As has been found out recently, all wilderness equivalents of workshop crops (i.e. melons and pumpkins in non-workshop locations) are piling up a large number of invalid markers over time. This is presumably related to cell resets: while the script on the crop resets its myDamageHelperRef variable to the default value of non (forcing it to create a new damage helper on firt load after a reset), the old helper apparently persists because it is never unlinked from the crop.
A fix for all remaining issues is outlined in the last posts of this thread:
http://www.afkmods.com/index.php?/topic/4551-mysterious-tatos-another-arrow-in-the-knee/