What I've seen of grass deterioration so far:
- Grass grows when flowers are on it and watered
- Grass grows after rain/ snow
- Grass deterioration does not occur under patterns, nor does it seem to grow. Patterns seem to freeze the grass
- Running does not deteriorate grass very quickly. For about 2 weeks I ran up and back on a stretch of ground for 5 minutes, I had planned to see how long it would take to deteriorate: I noticed no difference (The study stopped after that because I lost my town...) I will be doing this again at some point.
Long story short: Grass deterioration is not much to worry about: run to your hearts content!
I think I mentioned this quite a while back. But isn't it great info to have?
On a side note, I ran into these at a gacha machine yesterday.