Why do cockroaches keep coming back

Because the treatment reached the ones you saw, not the ones you did not. Cockroaches are seen at the edges of a population, so spraying a sighting removes a fraction. Until the harbourage is found and treated, the population replaces what was killed.

What actually happens

• The sighting is the edge of the population, not its centre.
• Harbourage is warm, dark and close to water: behind cabinetry, in ducts, under appliances.
• Neighbouring units matter in shared blocks; a treated flat next to an untreated one gets re-colonised.