Context: I am using a software package called Social Engine. It is extremely buggy.
Anyway, I asked (paid even) the Social Engine people to do an upgrade and when
I have, at the top of my .htaccess file
Header set Accept-Ranges none
RequestHeader unset Range
hope this helps.
Intercept the headers coming back from your ISP and verify that you're getting a 416 status code. If so, intercept the headers you are sending to your ISP and drop the range header; this should force the server to send you the entire file.
The issue could be due to your browser having cached the original CSS files and trying to request byte ranges of the new files. See for example this bug with Chrome.
As far as disabling range requesting, it might not be necessary if you clear your browser cache, but if you need it you could try the following Apache config:
Header unset Accept-Ranges
This will tell clients that they cannot use the Range
request header to request byte ranges of your files.