What is the error? Do downloads fail to start, fail to complete, become corrupt, fail to open, disappear, etc? What type of files are you downloading? Can you approximate their size? Over what type of connection are they downloaded? (3G, 4G, Wi-Fi)
I haven't had any trouble with downloads in the native browser, but I encounter difficulty everyday with apk installation.
I remember reading in another thread on another forum of someone with the exact issue, not being able to download via the stock browser, and they fixed it by using the file app Astro File Manager. Seems there is an option in Astro's setting that enables downloads in the stock browser. I don't have Astro installed so I can't check this - just throwing it out as a possibility.