[verb て-form] + いる + 最中に [noun] + の + 最中に
最中に means "right in the middle of": something happens while an action is at its height, and usually interrupts it. A verb goes in the ている form; a noun takes の.
The verb is never in the dictionary form: ×食べる最中に → 食べている最中に.
The second half is something that breaks in from outside – a phone call, a noise, an accident. Something that was going to happen anyway doesn't fit: ×勉強している最中に、十時になった.
With だ or です, 最中 ends the sentence: "I'm in the middle of it." It explains why you can't stop or talk now.