It's important to keep an open dialogue going with your child's teacher about how he is progressing in lessons. This is true for children of all ages, but especially for really young students. If, after some lesson time has transpired, your teacher feels it is best for your child to stop lessons for a while and wait a bit before restarting, it generally best to accept that advice, rather than force the issue or create a negative experience for your child. Wait six months to a year before restarting lessons. In that event, no one has failed and it doesn't mean your child will never be ready to begin lessons. Nothing negative should be thought of the concept of waiting a bit to restart lessons. In the meantime, keep the music flowing at home, let those notes continue to be heard. Then you can restart your child's lessons a little later with the child still having an interest and desire to learn.
If the previous exposure to music has been going on for a long time, and if the parent(s) have reasonable expectations for their child taking lessons, it should be a positive and life-long endeavor for all involved. Always feel free to communicate honestly and openly with your child's music teacher, if there are any misgivings or questions about what should be done, or if things are not going as smoothly as one would wish. However, please keep in mind that most of these discussions should probably be done away from the child, perhaps setting up a separate time for a phone consultation or personal time with the teacher sans the child.