Hi,
   This is about the new org-table-header-line-mode, which is very useful to me, thanks.

Attached is the smallest file I could create to reproduce this issue. Steps :

1. emacs -Q
Latest Emacs cloned and built from master today.

2. Open the attached file

3. M-x org-table-header-line-mode

4. Resize emacs window very small such that horizontal as well as vertical scrolling is required to see it fully.
Otherwise, add rows and columns in the org table in the file such that it exceeds window size both vertically and horizontally. This is not a useless example because the header line mode is most useful when you have a big table and heading scrolls off your visible window.

5. Go to end of line in a row in the table when the header line overlay is active.

6. Press C-n  (or down arrow) twice

Observation : cursor is at the beginning-of-line

Expected : cursor should remain at the same column as earlier

=========
My unsuccessful code analysis, if anyone is interested :
There is a post command hook to update the overlay of table header. This includes the function "beginning-of-line". In more recent versions of org, it is (move-beginning-of-line 2).

But all instances of "beginning-of-line" or "move-beginning-of-line" are wrapped in "save-excursion".. In fact if I invoke (org-table-header-set-header) instead of C-n, the cursor does not go to beginning of line.

thanks
Oorja