I'll tell you the way I did it with my Doberman. Instead of giving him an opportunity to break the stay, I reinforced him for tiny, baby successes. First he has to learn to stay for a reasonable kind of stay, both sitting, standing and down. He has to get that first.
What I did was start in an area of practically no distractions, my living room. I think the mat or his own rug is a great idea, although I didn't do that. I started out by breaking it down, just as I did with the regular stay into duration, distance (between him and me) and distractions. Those are really the three parts of stay.
So, while I concentrated on duration, I relaxed the distance....meaning, I stood fairly close to him. For the duration, to help him succeed, I would give him a good treat frequently and would say, "goooood. stay." (just to remind him that the exercise wasn't over) Gradually, I lengthened the intervals between reminders and treats. This way, he is unlikely to break the stay. The more he breaks the stay, the more he learns that he can break the stay. The more he is reinforced for holding the stay, the more likely he'll want to stay put.
So, after he's good at staying in the down with you fairly close, you can then begin to step back, further and further, gradually, lightening up on your duration criteria for a while. Practice going further back and returning to him. (never call him to come from the stay...not for ages and ages, till he's very solid) Go to him. When you get back 20 ft or so, don't make him stay for long...return to him and give him a treat and praise....a little reminder, "stay" to make sure he doesn't think that he can get up. Then give a release word when you want to end the exercise.
For the first few days or week, practice just the first part...the duration. Then do the other, the distance from dog to you. Then put them together. Start out not so long and not so far away and reinforce. Gradually increase both. You can add in a few distractions here. Or you can add in a few distractions after he gets solid on either the duration part and the distance part. Or add them in in both places. Just wait until he's got a handle on the duration or distance.
I did this and then moved to my pasture when I used a tree to hide behind. (that was for the out of sight long down) I'd pop out often and praise him, remind him, then go behind the tree again. I'd walk to him and give him a treat. Tell him that we're still doing this, so "stay" and I'd again walk the 20-30 ft to the tree and go behind again. Gradually, I lengthened the time.
You don't want to have to remind the dog or repeat commands for too long. So, you can fade all those little reminders as he becomes more proficient.
My idea is to set him up for success. Prevent failure by making it easy for him at first. Reinforce with a yummy treat and calm praise FREQUENTLY for baby steps. Behavior that you want MUST be reinforced consistantly for the probability of it recurring in the future.
This breaking things down helps all this and I think produces a very reliable stay.
30 minutes is really excessive. I don't really know of a practical reason for 30 minutes. If that is the case, then I think the dog should be allowed to chew on something or sleep. My dogs will stay for 30 minutes at dinner time if I have guests at the table. However, the only requirement is that they stay away from the table. They can lie down where ever and chew on their toys or even change their position or location. That's the only time they have to sort of stay for 30 minutes. But then, I don't do competition. But I have my dogs stay for real life purposess which have to do with my life style.
edit: Just a note: If your dog breaks the stay, it means you've asked for too much too soon. Go back to where he was successful and work there some more. Try not to move ahead to a more difficult phase until he has a good handle on the previous phase. For instance, if you've worked your way back to 20 ft away and have him staying for a minute and he breaks it, go back to the duration he was able to hold it OR go back to the distance where he was able to tolerate the full minute. Maybe you were only standing 6 feet away from him. Dogs don't generalize very well, so that is why it is helpful to get him good on duration, say...first, then the distance, then put them together and sneak in a small distraction, once he gets that good.