The problem is in the second dialog (code below). When there is no first confirmation dialog on the parent page, OnAfterRenderAsync (second dialog) is executed only once.
When there is the first confirmation dialog on the parent page, the OnAfterRenderAsync of the second dialog is called more than once, finding DialogService.Close (null) in the reenderization.
To solve it, I transferred DialogService.Close (null) into if (firstRender). But, it is something for an investigation.