Hey Vinayak, that's because mediafire is integrating captchas. So actually the password it asks is the captcha I think.
After a number of downloads they ask for a captcha, and then you're good again for a number of downloads (in my case it was after 100 downloads they asked it once).
If you just open one of them in your browser and enter the right captcha you should be able to continue in JD again. At least that worked for me.

But please go into JD chat next time it happens, then you might be able to help the developers to create a solution for it.