When the Copy Records command from the table context menu is used, a table can't be pasted into another data frame. Layers, however, can be copied between data frames by choosing the Copy command from the layer context menu and the Paste Layer command on the data frame context menu.
This is because the Copy Records command works differently from the Copy command for layers. Copy Records can be used to copy the records of a table in a tab-delimited format so they can be pasted into other applications such as Microsoft Word.
The table must be added to each data frame separately.