There are a number of reasons why a student is having problems.
1. Kid being forced to play by parents / No desire to play therefore he won't try.
2. Not practicing enough / (We live in the age of instant gratification. Many kids don't understand that some things really require work.)
3. Being tone deaf. Some people have trouble hearing the difference in pitches. This translates into problems with playing those pitches. (They may think they are playing the right pitch or not notice the difference.) This requires a lot of ear training to overcome this. It also requires the teacher to be creative. Checkout Clyde Hunt's webpage http://www.bflatmusic.com Clyde has some wonderful ideas and items that help this kind of problem. He has written songs in the range that problem students play in. This keeps them motivated and trying.
4. Not understanding that they change the pitch with the lip muscles. The student has to understand what you want them to do.
Mendez used lip buzzing to teach embouchure and aperture control. He buzzed simple songs and scales and had his students practice that.
Stevens used a pencil between the lips as an exercise and a visual guide. If the end of the pencil was pointed down the chops were set for a low note. If it was pointing up the chops were set for a high note. With kids a quarter works as it is easier for them to control.
Have them try to play a Hoseaphone. In the normal trumpet length they may have trouble. If you increased the tubing to 6 feet they should be able to play 2 or 3 harmonics. This is used to show them that the chops play the horn NOT the valves.
5. Faulty embouchure setup / poor mouthpiece placement.
I like close embouchures. That means lips are touching. Some kids (and adults) create a hole between their lips before they play a note. With untrained chops this is difficult to overcome. Have them let the lips touch.
I like buzzing the lips and sneaking the horn into playing position. If they are buzzing the lips are touching. Doing this for every note for a few days will cure this problem.
I like to have the player center the buzz into the mouthpiece when they sneak it into place. That takes care of bad placement.