Some "Christians" aren't true Christians. Which is fair enough, I think, if my question is specifically why Christians disagree. There's a more general point though, of which more later.
God chooses to interact with humans in a human way, as exemplified by Jesus. He never promised to give people a way to tell who was right. A quick read of the Bible shows that God didn't always interact in this way. Even in the New Testament, we're promised there will be signs accompanying those who believe, some of which I'd find pretty convincing if I saw them: I'd certainly respect the religious claims of people doing that stuff more than people who don't, because they're showing they can do something inexplicable which is at least worth investigating. Any Christians volunteering to drink poison? ;-) Edited to add: robhu rightly points out that textual critics say this passage has doubtful provenance. Evangelicals generally say the Bible is inerrant "as originally given", which raises some other questions, since there's scholarly debate about what was in original manuscripts. Edited to further add: John 14:11-13 promises that whoever has faith in Jesus will do even greater miracles than him, so the odd amputee healing doesn't seem too much to ask of Christians.
What is noticeable is that God seems to do special effects less and less as we get closer to the present time. Edward Current argues that God's ability to hide shows how powerful God is, and that God is testing our faith, but, despite his obvious sincerity, I'm not convinced. I think there might be a simpler explanation.
God wants people to know him rather than treating him as an encyclopedia. I suppose the objection to treating God as an encyclopedia must be that it is impersonal, rather than an argument that having access to correct information actually impedes learning. So let's imagine a world in which God was not an encyclopedia but a teacher of Christians, a good sort of teacher who made the lessons interesting but didn't let fights break out in the classroom. Does that world look like this one?
Aren't you just asking why God doesn't announce his presence? I suppose I am. Annoyingly, someone has got to that question before me and made my arguments better than I can. The brilliant Richard Carrier's essay Why I am not a Christian (not to be confused with Bertrand Russell's essay of the same name) contains a section called God is Silent which points out the contradiction between what Christians say God is like and how he acts. Go read it.
My arguments about Christians and their relationship with God are, as my correspondent rightly says, a special case of the general argument that God is silent. Talking about Christians specifically negates one of the common defences against that argument, namely that if God were too obvious, it would do away with free will. But Carrier points out that such defences are ad hoc: who thought to mention that God values free will above almost everything else before people started debating the problems of silence and of evil? What is the evidence for this? If you're evangelical, where does the Bible say that God values free will so highly? Christians can't even agree that people have it, let alone that God values it.
God's silence, and his entrusting of what we're told is a very important rescue mission to a bunch of people who are pretty bad it, are pretty powerful arguments that he's not there. If I saw any amputees miraculously healed, though, I'd certainly reconsider.