When inserting a row, regardless of the CopyOrigin, Excel will only put vertical borders on the inserted cells if the borders above and below the insert position are the same.
I'm running into a similar (but rotated) situation with inserting columns, but Copy/Paste is too slow for my workbook (tens of thousands of rows, many columns, and complex formatting).
I've found three workarounds that don't require copying the formatting from the source row:
Ensure the vertical borders are the same weight, color, and pattern above and below the insert position so Excel will replicate them in your new row. (This is the "It hurts when I do this," "Stop doing that!" answer.)
Use conditional formatting to establish the border (with a Formula of "=TRUE"). The conditional formatting will be copied to the new row, so you still end up with a border.Caveats:
Set the border on the inserted row in VBA after inserting the row. Setting a border on a range is much faster than copying and pasting all of the formatting just to get a border (assuming you know ahead of time what the border should be or can sample it from the row above without losing performance).