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I'm a novice coach and don't understand why a program can work perfectly well one day and the next with no alterations not work. Also, why does the robot occassionally stop in the middle of its run?

First of all, Aloha!!!

Second, welcome to the world of electronics and programming. Lesson here is this is why we need more people to know what it takes, not for the appreciation but to somehow give them enough so they can help the field. Scientist build their own robots, with help, and there are a lot of things that can work one day and then fail the next for some reason. Electronics and programming can be very finicky. No easy answer but here we go with the troubleshooting:

Because your question is open there are many answers. What needs to be determined first is the sensors your using and programmed for, and what conditions are before you.

Sounds like programming error if I am not mistaken. But how your team built the robot can be a factor.

Assuming you had a good first run and everything worked.

Mechanical and electronic aspect first:
1. check to see that one side is not weighted more than the other, this will cause your robot to turn.
2. check for bushings or other parts that may be too tight. This too can cause your robot to move funny.
3. Check to see if things are blocking sensors or causing sensors to miss read, like the ultrasonic sensor for example. It can send out a signal that is conical in shape and a single piece of something, on the robot, can be in the way of the signal.
4. Check to see that all parts were put on well and that the robot is not wobbly. Wobbly robots can cause miss readings.
5. Make sure the lighting is always the same for light sensors. A little ambient light can throw off the whole thing. Use lego pieces to block out any ambient light.
6. Moisture and/or heat can cause your NXT to not respond the way you want.
7. Check your board for slipage. If your rotation sensor is the problem, check for slippery spots on the board or slipage in your device. This can cause miss readings.
8. Finally, check battery power. It is well known that batteries with 80% or less have not reacted correctly for some unknown reason. I think from my tests it was more like 75% or less.

Programming:
1. By now you and your team should know their own program. The program can be sectioned off by isolating events that are happening. By events I mean, in a simple program to move forward, hit the wall, and move back, three events were identified through my simple Pseudo code. The first is to move forward, the second is the hit, and the last is to react by moving back. Behind each event I would place a sound block. I start low on a Diatonic scale (C scale) - have kids ask band director if you don't know Diatonic scale - then work my way higher. So I would use three notes to identify where I am in the program. Example, robot drives forward use the notes "C" (in this loop of driving forward I would put the first note that would repeat over and over, or if not a repeat and its a wait then it would play once which means I would put the sound block in the front of the drive forward block). When the hit occurs I would have the sound block right after playing the note "D". When the robot moves back play the last note "E" to identify the move back. If something goes wrong I'll know just by not only watching but by listening to the notes. I know three notes will play, I also know that the first note is low and it goes up the scale after that (goes higher). We don't have the luxury of using different lights to indicate where in the program something went wrong. So sound has to do.

2. Since you've done the Mechanical and electronic part of the check and everything seems ok, go and do this. Highlight and copy the whole program on to a new workspace and save as new file. Sometimes things can go wrong. Although you didn't indicate any last minute changes, at this point you've done all other checks and nothing worked so far so doing this ensures a fresh start with no corruptions. There is a however in this, if one of the blocks is no good then the whole program needs to be written over again on to a new workspace. Be sure to shutdown the computer and leave it off for 12 seconds to dump and erase memory and then turn on again to give you folks a fresh start.

NXT:
1. If you're here, then it is time to scrub the NXT and reset. There is a pin hole under the USB port of the NXT. In the pin hole is a RESET button. You will have to hold that button down to do the RESET. Contrary to LEGO instructions.
a. Turn on NXT.
b. Press reset with unfolded paper clip.
c. Hold for 10 seconds.
d. Let go and leave it.
e. Wait for a minute then try turning it on. If it doesn't repeat above steps from "b".
f. Through you NXT-G programming software check to see if the memory is now empty. If not, empty it completely by deleting all programs. Not system files though.
g. Program your NXT.