She's pretty good at hiding her intentions. She will come in, I'll watch her like a hawk, then she'll go out, and several days later I'll notice poops on the rug. Working backwards, I can usually figure out roughly what day she did the deed, but even so, it's slipping by our vigilance net a lot of the time, so I know she is getting good at doing things surreptitiously. The main thing we are finding so far is that even if she has just been outside for a long time, she apparently is coming in ready to poop.
It also helps, since you know where she goes to have her poop that you interrupt as soon as she looks like she's going to do it there and take her straight outside and then praise her when she poops outside instead.
It's that combination of interrupting the unwanted behavior and praising the wanted behavior that's worked out the best for us and my Fedora (a 1 year old mutt), she's so determined to use the outside as the bathroom that she didn't even want to go inside a training rink where we went even if all the other dogs were all "oh, there's ground in here, I suppose that means it's the bathroom", she still insisted to be taken outside before she'd even pee.
I think brightday3 has hit the nail on the head. Training is all about rewards for good behaviour as well as consistency and vigilance. First, both rugs will now have his smell on them, so if I were you I would take them up and place them somewhere safe for the time being. You should also have them properly cleaned and disinfected before you put them back, so all trace of your dog's scenting has gone. Next, vigilance ... make sure that you observe your dog when she goes outside first thing in the morning and as soon as she does something, praise her. Then, preferably every hour, let her outside and observe her until she does something - then praise when she does. Make sure you let her out as soon as she has eaten and watch her until she does something, then praise, praise, praise.
She will get the conection eventually. Some dogs just take a little longer than others. Good luck. Tony
I had a similar problem with my puppy, only he kept wetting in the house. I also kept him in a crate. I took him to a puppy class, and his trainer said, that when ever he did his business outside, I was to praise him and give him a small treat, so he knew this was the desired behavior. After a couple of months, I realized he had not wet in the house for a long time. The only down side is, he always needs a small treat when he comes back inside. But I think the trade off is worth it.