The method you were using was the insertion of a TIME field. This is really a variant of the DATE field which is good for showing the date or time that is NOW but not good for much else.
Using Date Fields in Microsoft Word
There are a number of fields that handle date and time. They can be very useful, but none would give you a time stamp that would stay unchanged when you insert a number of them at different times.

A TIME or DATE field can be locked so that it will not change, but this is an additional step. Such a field can still be unlocked, in which case it will lose its value. It can also be unlinked. That would change it to plain text.

The macro method is superior for your purposes.