At least Peter and Valentine had a Monitor too, though not as long as Ender had his. As Graff tells Ender that there were or are others like him, it's plausible that these had Monitors too, before joining the Battle School.
The Monitor is described as a tool for screening candidates for Battle School. The way the doctor at the beginning of Ender's Game talks about it, Monitors seem to be common enough. At least he knows exactly how to take it out which indicates he did it at least a few times in the past.
The screening is most likely a pretty resource intensive process as well, because the candidates are watched 24/7 and evaluated all the time (or at least they make it sound like this). It's also possible they only watch those who are supposed to be the very best, like Ender, because of this.
As too why the Monitor is never mentioned again in Battle School, one out of universe answer might be, that it was simply a tool for the writer that served it's purpose on the initial pages and was of no use afterwards.
But there are also some possible in-universe answers.
For one, the doctor tells Ender that he will still feel the Monitor for a while, although it's gone. A phantom feeling that will go away in time. It's possible that all the kids simply no longer remember or care about their monitor. They are quite young after all and forget such things much faster then an adult would
If everyone in Battle School was indeed screened with a Monitor before they were accepted, it might also be such a common thing that they don't consider it something worth talking about.