Watched a docu series a few months back which concentrated on about 3 pest controllers who were all female. In one of the episodes, an actor's house was infested with moths and it was quite a process to get rid. You say that no sooner have you killed them, than another lot arrive which may suggest that they have laid their eggs in your property. One of their preferred laying areas is carpets and their offspring will feed on it's fibres, so check for any frayed areas and hoover thoroughly and regularly. Smeone may be able to provide you to a link to the programme which, i believe, was titled, The Ladykillers, Pest Detectives and was aired on BBC 2.