How often to wash hair?

So naturally my hair is like a dark blonde / dirty brunette color. I recently dyed it like a dark red / auburn color. I’ve found this particular color fades VERY quickly! So Im gonna have to switch up my shower routine if I want to keep this color long term. I’ve found it starts fading roughly about a week to a week and a half if a wash every day. So now I’ve cut it back to washing my hair maybe every 3 to 4 days. When I shower everyday I wear a cap, and to keep it looking nice on non wash days I use dry shampoo snd hair masks! Is this too long to go without washing? I’m really just trying to keep this color from fading so fast