We have a 12 year old lime tree that produces fruit regularly but for at least the last 5 years it has had a problem that I just can not shift. I have posted photos of back and front of old leaves and relatively new leaves. The underside of some old leaves are covered in white blotches that appear to be minute insects (slightly smaller than the eye of a needle) but I have never seen a single one move! The top of the leaf shows yellowing above the underside white patches. In exceptionally bad cases there appears a tiny (1mm) cotton wool effect around the edge of the leaves, a little like wooly aphid but much smaller and less prevalent. When I rub the underside of the leaf the white rubs off leaving little mid brown scars.
Against the old leaf I have placed a new growth, maybe a month or two old. It has the beginning of identical white insects but strangely these are both sides of the leaf.
For the last year I have twice sprayed the tree with a course (3 sprays a week apart) of NewMectin a systemic insecticide and tried Kocide a copper based fungicide. In previous years I tried Caprid. They seem to cut the infection back a bit but never clear it.
Name: Carol Santa Ana, ca Sunset zone 22, USDA zone 10 A.
It does look like some type of Scale or Mealy bug, though I've never seen that webbing from either of those. Have you tried spraying with Insecticidal soap, or rubbing alcohol ? I'm not familiar with that systemic you used, but it does take awhile for the tree to take it up, even if it's properly applied, which it often isn't.