I am an organic gardener ... so I don't use chemical pesticides.
On my greens what I usually do is start a bed, and let them grow and harvest up until they start getting buggy. (and they do get buggy after a while) Then I will pull it all up and put in compost pile.. I will break that bed up again and wait a couple weeks and replant it with something else (crop rotation).
5-6 weeks after starting the first bed I will start another in a different location... and when the first bed gets buggy and pulled.. the second bed is still in good shape and produces for several more weeks before getting buggy.
You can keep two beds going like that, alternation locations, and keep the greens going.
I got some aphids and white flies now on my tomatoes... when you have all of that fresh green growth, whether it is tomatoes or greens, critters are going to come on. Not much you can do about that.
While looking for a organic solution to aphids I ran across this one.. A guy at a local Farmers Co-Op recommended it. He said their organic gardeners report that it works really well, especially on soft bodied creatures and caterpillars.
It's called captain jacks dead bug. See amazon link below.
Below are some details on the active ingredient.
Contains Spinosad, a naturally occurring soil dwelling bacterium that was collected on a Caribbean island from an abandoned rum distillery
It gets 4.5 stars from Amazon reviewers (88 reviews).
I am trying it on my tomatoes now.. and when my next green patch starts getting buggy I am going to try it out on them too. It is usually caterpillars that end up wiping out the greens and it is reported to be especially good on them.
I read thru the documentation and on most fruits and veggies it says it is safe harvest 1 day after spraying. I would probably wait a week myself just to make sure.
Spinosad kills insects via hyperexcitation of the insect nervous system...
It does not kill immediatly, but once ingested by the critters it makes them hyper-excited and they expire from exhaustion after a period of time.
Reported as very save for human beings... but not will kill bees (honey bees)... so consider that. Don't usually have much bee activity around greens (unless they go to seed and flower).
I am just experimenting with this new organic solution myself, so can't really brag on it yet. In a few days I should know how it works on aphids and white flies.
Good Luck !