If they're back within a week them they must be in the environment and just jumping back on the birds again. He must be missing somewhere or not spraying properly. Or else, a ground area isn't sprayed effectively and they are making their way back up. The flea needs to be able to dig into the soil for a stage in their life cycle. As your shed has a concrete floor it should be easier to deal with.
I have to admit that I have sprayed my sheds out with Maldison before, even though it is a nasty toxic chemical. I don't recommend it because there's more potential for problems with it, but it does work. I would always use a newish container of it (not an old one out of date) and follow the manufacturers directions. I think persisting with Permethrin is safer and better option, but it depends on how you feel about it.
If the problem is driving you mad you might want to pull out all the guns. Remove all the litter, clean everything out, spray everything out with your choice of product, spray your birds also (don't get any in beaks or eyes!). You could give them a dose of moxidectin as well if you think there's a chance some have been missed. You should redo permethrin spray in about about a month or if it rains.
I'll copy it here.
Stickfast fleas of poultry
The stickfast flea is one of the most troublesome parasites found in poultry.
It is a serious pest, as large numbers may cause progressive blood loss, loss of condition and sometimes death.
Description and distribution
Stickfast fleas are easy to recognise, being reddish-brown and smaller than other fleas.
They 'stickfast' and don't move around like other fleas.
They are seen mainly in warmer areas and can survive extremely low temperatures.
Understanding the life cycle of the stickfast flea (Echidnophaga gillinacea) makes control methods easier to understand.
The average life cycle is about 4-5 weeks depending on seasonal conditions.
The cycle starts with the attached female laying eggs, usually during the hours of darkness. Adult fleas live for about 6 weeks on the host laying approximately 12 eggs per night.
These eggs fall to the ground and hatch into larvae that feed on ground litter.
Approximately 2-4 weeks later the larvae burrow into the soil to a depth of 15 cm and form a cacoon.
They particularly like sandy type soils
From this cacoon emerges an adult flea within 2-3 weeks depending on temperature and humidity.
Adult fleas that are unable to find a suitable host can only survive for a short period of time.
Effect on poultry
They bury their entire heads into the host and spend days attached in this manner
The most common spot for the flea to attach to is the head of poultry, the eyes and face as black as eyebrows.
Other sites for infestations are under the wings and on the breast.
A heavily infested bird can carry a black mass of fleas on its comb, wattles and behind its head, eye lids, ears, under the neck & down the neck.
Effect on other animals
Stickfast fleas can also infest other birds (ducks, pigeons), cattle, dingoes, kangaroos, rabbits, rats, goats, cats, horses, dogs and sometimes man.
Control and treatment
Control and treatment go hand in hand.
Smear a light coating of an oily substance over these insects and they suffocate very quickly. Olive oil and baby oil are useful for this, as they do not irritate the birds' eyes.
Treat the shed floors as for mites and ticks.
Like mites, all fleas will infest your home if left unchecked and will feed on any living warm-blooded animals.
Infested birds should be sprayed with insecticide and all litter or articles harbouring the flea destroyed.
In controlling the flea on poultry, the housing of these animals must be included.
For this reason, the parasite is not easily eradicated from backyard poultry houses or free-ranging poultry farms that are unable to provide impervious flooring.
Impervious floors are necessary for breaking the life cycle by denying larvae the ability to burrow 15cm into the soil to form a cacoon.
Applications of organic oil based products (neatsfoot oil, linseed oil, castor oil, olive oil, baby oil) or dressings including petroleum jelly or parrafin oil will suffocate attached parasites.
Treat the skin with Maldison solution or Carbaryl dusting powder.
Use of these chemicals must be in accordance with the manufacturer's label.
Cages, pens, perches and surrounds
Spray with a solution of Maldison.
The chemical application of Maldison must be in accordance with the manufacturer's label.
Treatment of housing and birds with insecticide should be repeated weekly until the infestation is completely controlled.
Keep a close watch on your birds and their environs and you will stem the tide of any creepy-crawly critters that may decide to make a restaurant in your chicken house.
Reference source and other personal reference sources used in this article
They also seem to be a lot worse at the end of summer. There will be a natural reduction in numbers as the season changes.
: a mild infestation. seen along the eyebrow.