I have had many problems in the past with trying to download larger files through browsers. You can open up a terminal and use wget.... with -c option. If it stops downloading at the 2 GB limit you have been reaching, just up arrow to the last command you just entered, and hit enter again. Your download will resume.
wget -c <download url goes here>
Here I am downloading a small DVD as an example. (I know it's not larger than 2 GB's but this will work regardless of file size, as long as you have remaining disk space to download it to).
I hit CTRL + C to stop the download.
I up arrowed to the previous command, and after hitting enter, the download resumes!
Hope this helps!!