Hi Silvia,
I've hired a team consisting of a property manager, a handy man, a gardener, a full time housekeeper, a backup housekeeper (soon to add another), a babysitter and a cook. Their performance has been great. We're on the Atlantic Seaboard and the team would be more than capable of handling a flat, depending on where it is and how big it is. The bigger the better, but if it is a small place I'm happy to recommend reliable people.
I chose to build the team myself because we were using an agency that weren't doing a good job, and it got to the stage where, if I didn't pay personal attention then things would entirely fall apart. So I sympathise with your question! Then my friends also had problems with agencies and ended up doing it themselves or stopping Airbnb altogether.
Let me know if you would like to discuss this further.
Cheers!
Lunda