I also adopted a Chihuahua male dog, I found him running around with a pack of chihuahuas (quite a sight). He's the same way. But I don't live with him anymore, being at school, I visit my family once a week.
As soon as my car enters the apartment complex, my dog knows I am there, and becomes super excited to see me. So yes, they have to have long term memory (I read somewhere that they have only a five-minute memory. That has to be crap.)