What is the difference between the download pause-able and un-pause-able files?

Solution 1:

The server would need to support the ability to serve partial content and handle partial requests. Most modern web servers are able to handle it unless you are using something that you built in-house.

You can get more information by reading this Apache document and the relevant RFCs. From the document linked - an example of a response.

HTTP/1.1 206 Partial Content
Date: Wed, 15 Nov 1995 06:25:24 GMT
Last-Modified: Wed, 15 Nov 1995 04:58:08 GMT
Content-type: multipart/byteranges; boundary=THIS_STRING_SEPARATES

--THIS_STRING_SEPARATES
Content-type: application/pdf
Content-range: bytes 500-999/8000

...the first range...
--THIS_STRING_SEPARATES
Content-type: application/pdf
Content-range: bytes 7000-7999/8000

...the second range
--THIS_STRING_SEPARATES--

Solution 2:

A common one is a lack of a content-size or content-range header. Perhaps the author forgot to set one in their download script?