I've just been testing it (in Hauptwerk v6, but v5 should be the same) and it seems to be working properly for me.
In my test I turned on the 'Diagnostics: log all MIDI messages ...' option on the 'General settings | General preferences | Advanced ..' screen tab, loaded an organ, configured a four-byte custom MIDI sys-ex message on the settings screen, then tried clicking the 'Test: send message now' button repeatedly. The relevant red 'Console MIDI OUT' virtual MIDI activity LED flashed correctly on Hauptwerk's 'Audio, MIDI and Performance' large control panel) as I pressed the Test button each time. Also, after each press, I used 'Help | View activity log', which showed that my test message had been send correctly each time. For example, after pressing the button three times in a row, the log showed that the message had been sent three times:
2021-05-31-12-49-48: INF:2564 Diag: OUT: MIDI system exclusive/raw: port: Console MIDI OUT 01 [=> FW AP MIDI], number of bytes: 4, bytes (as decimal): 240 002 046 247, bytes (as hex): F0 02 2E F7.
2021-05-31-12-49-51: INF:2564 Diag: OUT: MIDI system exclusive/raw: port: Console MIDI OUT 01 [=> FW AP MIDI], number of bytes: 4, bytes (as decimal): 240 002 046 247, bytes (as hex): F0 02 2E F7.
2021-05-31-12-49-55: INF:2564 Diag: OUT: MIDI system exclusive/raw: port: Console MIDI OUT 01 [=> FW AP MIDI], number of bytes: 4, bytes (as decimal): 240 002 046 247, bytes (as hex): F0 02 2E F7.
I also then tried reloading the organ and trying the button again, and it still appeared to be working properly each time (virtual Console MIDI OUT LED flashed, activity log showed message had been sent).
If you try that test, do you get the same results?