Does rosemary even get sick?

Does rosemary even get sick?

I have a potted rosemary plant that's been having random leaves yellowing and dropping off all season. I thought it was lacking in nutrients, but several applications of fertilizer haven't affected it at all. Also, before falling, the leaves develop purple specks that leave the surface looking like a mosaic. I can identify most common garden diseases, but I never hear about rosemary coming down with problems the way roses or tomatoes do. Anyone have thoughts on what it might be? Should I cut the plant out and try another one next spring?
my grandfathers garden

my grandfathers garden

Please tell me what this plant is?

Please tell me what this plant is?

Grocery List Help

Grocery List Help

Hollyhock

Hollyhock

Help identifying plant

Help identifying plant

Now some veggies.

Now some veggies.