DNN 4.4.0 introduced compression and it is turned on by default. This causes problems with downloads of files and images.

Go to Host->Settings and uncheck the 'Use WhiteSpace filter' checkbox in the Performance Settings section. Click on Update, then click on Restart Application.

That should fix your download problem. If not, go back to host settings and try turning off compression completely.

Make sure to Restart the Application in order for the compression changes to take effect.

Just thought i would comment here that you can use both Compression and Whitespace Filtering in DNN 4.4.0.

Change the default Whitespace Filter to a less aggressive expression listed below:

(?<=[>])\s{2,}(?=[<])|(?<=[>])\s{2,}(?= )|(?<= )\s{2,}(?=[<])

And for the Compression, you may need some addiotional entrys to the Exluded Mime Types list. Here is what i have been using below:

image/gif
image/jpeg
image/jpg
image/png
image/bmp
application/zip
application/x-zip-compressed
application/x-gzip-compressed
application/x-compressed
application/octet-stream
application/pdf

I upgraded my DNN 3.3.2 site to 4.4.0 and have been running the Repository Module just fine with those changes.