I think they hint at this multiple times, such as during the conversation with Robert about if Hades (the realm) still exists, and during the conversation with Hermes when Asterion is worried about Hades and Hermes tells him Hades is fine. Hades and his realm remains stable because of the undying population that will still worship him and the other gods of the realm.
It might not only be based on belief/worship but might also take info account nature and technology. Wherever technology goes magic wanes and (in the case of Kota) when their home is contaminated they lose their powers/strength.
It makes me wonder if Hermes condition is a direct result of the MC bringing the internet to the hotel. The hotel is a realm Hermes oversees and it would make sense that while the MC drives out more of the magic it would cause Hermes rapid decay.