John, I rent my flat here in Luxor on a long term contract (5 years) but there are short term lets available in the same building. All of the seemingly "holiday" lets will probably be available for long term at a much reduced rate.
It all depends on where exactly you want to live, but even the Red Sea resorts will have many apartments for long term rent.
I do not know of any agents in the Red Sea resorts, but Mushtaq can probably help there, but I do know agents here in Luxor and there are also a number of "flat finding" men, who search for suitable accommodation, details of which are specified by you, on your behalf. They will also negotiate price and contract terms for you. I used one to find my flat, and it only cost me 100LE for his services and I got exactly the flat I needed at a price I wanted to pay, and no agents commissions to pay.