The actual problem being encountered here is that VB6 looks to the registry for some of its system settings. When you run the project yourself, VB picks up settings from your user. When Hudson runs as a service it logs in as Local System, which has its own registry settings.
The VB6 setting that is relevant here is Options/ErrorTrapping. By default the registry contains 'Break on All Errors'. The project in question requires 'Break on Unhandled Errors'. The symptom seems to be that VB6 locks up when an error is raised.
The solution involves exporting the relevant settings from my user and importing them to Local System.
There is an answer with a link about running regedit under Local System, but my answer is to use Hudson itself to run regedit as Local System. Also there is a question here about vb6 ide settings.
Use a Command Window to export VB settings from this key to a file like this:
regedit /e vbide-1.reg "HKEY_CURRENT_USER\Software\Microsoft\VBA\Microsoft Visual Basic"
Create a new job in Hudson which does nothing for now, but click Build Now to create a job folder.
Find the folder it creates and copy vbide-1.reg to the 'workspace' folder there.
Configure the Hudson job to execute this Windows batch command:
regedit /s vbide-1.reg
Click Build Now again and the batch command should run. Verify in the Console Output:
...\workspace>regedit /s vbide-1.reg
Disable the Build, or just delete the project.