From the information provided, it would not appear that there's a problem getting the carpets to look clean.
The problem appears to be re-soiling. The obvious candidate is new soil being introduced. This will be from outside, the kitchen and it's floor, the staff's shoes will be grease laden, so will the wheels on serving trolleys.
I'm a little concerned about the early cleaning cycles. Generically speaking, a flourocarbon protector would be applied to an acidified carpet. This wasn't done. Again generically speaking, a protector needs 24 to 48 hours to completely cure, this is different to the drying time. This is not possible in a 7 day working environment. The protector may have turned sticky. Subsequent cleans may have removed most of this.
An extra consideration may be to pilelift and clean to industry accepted standards, finishing with an acid rinse. When completey dry, return visit to thoroughly vac/pilelift again.
Given the nature of the beast, the chances of rapid resoiling are high.
Being a synthetic face yarn, the fibres will not be as effective at hiding soil as a suitable wool fibre. There will also be surface abrasion to the nylon fibres. They will look bright and vibrant when wet, but opaque and dull when dry.
The carpet's colour, especially in this environment, will also affect the carpets appearance retention performance.
Safe and happy cleaning

Ken