Battling with broad mites; neem sprays not seeming effective.

[Doelman]

we can't help you without some pictures mate, we're just throwing darts at a board in the dark here 

 

[acs1]

The only thing I can really discern is that they're whitish in color and they move around quite a bit when disturbed.

 
Well, took this pic with my new microscope @ 90x after neem oil treatment. Neem helps keep them still for a good pic... lol
 
With no magnification they're invisible.
At 30x they were just a tan minuscule dot, barely noticeable with no discernible features.
Anything less then 40x is useless for broad mites imo. And more power will let you see details in their anatomy to confirm identity.
 
BTW, all these are dead mites on a leaf...
 

 

 

[Takanotsume]

As an update, it seems as though one part of the plant had a particularly bad infestation because the other parts are finally starting to put healthy new growth that isn't being killed by mites before it can develop.
 
Increasing the spraying frequency seems to have managed to (mostly) get them under control, though I'll probably prune away all and any damaged leaves regardless.
 
I also harvested my first Aji Limon pepper a day ago...though I can't say I was terribly fond of its flavor (It reminded me of lemongrass mixed with soap).