Arcane Eye doesn't disappear if you leave

[Dwarf_Hammer]

If you leave a level with Arcane Eye still active the eye tile remains in the same spot when you return.

[martinuzz]

That goes for all spells. When you leave a level, it is saved including any area spell effects. Their timer will resume once you re-enter the level.
It should be fixed, as it makes stairscumming even more powerful. Think casting multiple overlapping instances of the same area-damage spell. 10-Double retch is nice too