Looking at the hyperlink of the one you did manually, it is relative to the current document location ie.
../Refs/Clinical_5.4/AichingerG_2011,_Ross_River_vaccine.pdf
Because it starts with .. this tells the system to go up one folder level and then down in to the Refs folder.
The other hyperlinks (which fail) have the full path defined. Also, the direction of the slashes seems to vary although I'm not sure that this is important.
Is your secondary software failing to convert the hyperlinks because the absolute path is invalid but the relative path is fine?
Are you able to run this macro on your Word document to see if that cures the problem when it hits the secondary software.
Code:
Sub ChangeHL()
Dim aHL As Hyperlink, sLink As String
For Each aHL In ActiveDocument.Hyperlinks
sLink = aHL.Address
sLink = Replace(sLink, "C:\Users\iaman\Desktop\eCTD_Office_Software\IND_Source_Folders\YFV_IND", "..")
sLink = Replace(sLink, "\", "/")
aHL.Address = sLink
Next aHL
End Sub
If that 'repairs' the hyperlinks, you could customise the original macro to make the links relative on the first pass.