Popping Down On a Sit/Stay

Are you training for competition or just for normal everday good behavior? If the latter, I wouldn't worry about your dog slipping down while in a stay. To me that would just mean my dog is getting comfortable in the stay - sitting still takes quite a bit of muscle control. If you need to fix it, you certainly can... just do not click/treat for the down/stay, and "reset" the exercise - keep it to shorter stays and increase time very gradually.
 
The eye contact thing varies with individual dog's personalities... some dogs are very shy of eye contact, others are fine with it, and still others seek it out. Try to "read" your dog for signs of anxiety, lip-licking, yawning, ears pinned back, looking at you out of the corner of his eye or ducking his head... these signals would tell you he feels uneasy and you might want to take a more sideways approach with less eye contact.

Are you training for competition or just for normal everday good behavior? If the latter, I wouldn't worry about your dog slipping down while in a stay. To me that would just mean my dog is getting comfortable in the stay - sitting still takes quite a bit of muscle control. If you need to fix it, you certainly can... just do not click/treat for the down/stay, and "reset" the exercise - keep it to shorter stays and incre

 
I agree. I trained out of order. When I was first training a stay, it was from a down position. Now, when I say sit, he sits, if I say stay, he downs and stays. And I will accept that. With him, it's all in the eyes. So holding eye contact is a good thing. Plus, I'm teaching him "watch" me.

I won't comment on the actual clicker part of this question, since I'm very new to that myself.  A lot of help I am. []
 
In terms of the eye contact, my understanding is that you generally want to avoid looking directly at the dog during a "stay", though as jones said, it varies with every dog.  Eye contact is a means of communication in the dog world, and if you are making it, the dog is likely trying to interpret what you want next.  This is not what you want in the stay.  You want the dog to relax and stay put until you return. 
 
I watch my dogs out of the corner of my eye - looking just to the left or right of them, but never directly into their eyes - if they are "staying".  Especially with Blitz, who has "a lot of eye" (I think that's what the BC people call it []) I have to avoid eye contact or he will be over-thinking what I'm trying to tell him, and is more likely to break the stay and come to me, which he wouldn't do otherwise.  He is fully capable of staring into my eyes and giving me 100% attention for the full length of a 50 minute obedience class, and the only time I don't make eye contact is during stays.  I'm interested to hear if others have had the same experience.

Go see the video on "stay" at www.clickertrainusa.com.  That may give you some ideas about how frequently you want to go back to reward your dog for the sit/stay at first, so that the dog realizes it's the sit you want him to keep.  You can train lie down/wait, and sit/stay, so the dog has separate cues, if you want to.  I don't bother, but whatever works! []

Thanks for the replies and advice.  I look at my dog's eyes when I train, and I guess I will continue to do so.  He loves looking in my eyes, he looks at me like a leader.  However, with dogs that I don't know at the shelter I suppose it's a good thing not to.  I never thought about it before until now when I read about it in Patricia McConnell's "The Other End of The Leash."  spiritdogs, I've seen that guy's videos posted on youtube.  I'll take a look at the "stay" videos.  What I have been doing if my dog goes into a down after I say stay, I start over and tell him to sit again and then stay.  Is that okay?  Or is that not going to teach him anything?

What I would suggest is staying close enough to your dog that the presence of your body discourages him slipping into the down.  Even if you step back and come forward to reward again, you can do it quite quickly.  Gal Ziv's video does show him doing that with Sheena.

My trainer does not teach a stay at all.  He thinks it is redundant.  His opinion is that if you put the dog in a sit or a down, he should hold that position until he is released.  To me, that makes sense.