I also use FoxFire. In FoxFire, you should click Tools (on the menu bar). Then on the Tools drop down menu, click Options. In the Options window, click the General Tab. Then in the Download Section, make certain the button beside "Always ask me where to save files", is clicked. Hope this helps. I would guess that most browsers have something like this.
These directions are for Internet Explorer. I included a link where you can get embroidery catogories to file your designs in. I prefer to file by Designer/Digitizer so I don't get double designs. (I also have Firefox and Google Chrome and they work differently.) Select the format that your embroidery machine recommends and hit Download ~ Click Save ~ In this next window before you hit Save again select a file you want to save it to (a file that you have already set up for embroidery files to go into) ~ After you saved your file you can go back and on most sites you can right click and save a picture image also to the same embroidery file if you don't have a design viewer. Go to your files and find your embroidery file - there you can extract the design using a zip type files (several available). There are various ways to keep track of your design files and programs that organize and show the design image for you.
What server are you using? some of the browsers make it difficult to download designs. I have had the same problem and have had to experiment with different browsers. I use Firefox and the designs go to a "download" file and from there I can unzip or move to where ever I want. Hope this helps I know how frustrating it can be.
Does this happen on other sites too? Hopefully someone with good computer knowledge is being able to help.