Is there something wrong with the corn kernels that don't pop?
Popcorn kernels pop because moisture is trapped inside of a relatively gas-tight shell. As the kernels are heated, the water inside the kernel turns to steam. The shell of the kernel keeps the steam from expanding, so pressure builds up inside of the kernel until the whole things blows open.

If the kernel doesn't have enough moisture inside of it or if the shell of the kernel is permeable enough to allow the pressure inside the kernel to dissipate before it reaches the critical pop pressure, then that kernel won't pop. Ever.

So to answer your question, no. Take the popcorn off the heat before the popped kernels burn.