However, the one limitation is that if I ask it whether it has can see a tag, it will only respond yes once while the tag is present. For this project, I need to know if the tag is there whenever I make the request, even if the tag hasn't moved.
This tutorial (http://bildr.org/2011/02/rfid-arduino/) covers the concept quite well but there is no reset wire on my device. How can I get it to tell me the ID whenever I request it?
Basically with that reader you can't.
It is a function of the logic inside the reader. The token is constantly read but only the first reading is transmitted. Use another reader or build your own.
I suppose you could but it might not initialise until the token is out of the field, but I don't know.
The problem could be that it takes a few seconds to initialise on start up. You need to experiment with your reader. I did have a look on the web site and the answers to questions are best described as evasive.