How do I fix this and has the client actually been discontinued?
The desktop client will be discontinued as from Jul 30 2016 and will no longer work.
Presumably because of this it is no longer available for download from their website.
See the MediaFire blog post below.
Shutting down MediaFire Desktop, new desktop app coming
May 18, 2016
At MediaFire, we endeavour to always provide the best possible
experience for our users, this requires an intense focus on building
and supporting the features that can provide the largest benefit to
our users. We also recognise that the currently vibrant ecosystem of
cloud syncing clients provides many alternative choices for customers
looking for that desktop syncing functionality.
As such, we have chosen to discontinue development and support of
MediaFire Desktop so that we can focus on the development of a new and
improved Desktop app that will make storing and sharing your files
with MediaFire even easier.
This discontinuation of MediaFire Desktop will be effective starting
on July 30th, 2016. Beyond that date, we will no longer be providing
support for MediaFire Desktop which will cease to function.
All files that were synced will continue to be available to manage and
share through your account on MediaFire.com and MediaFire’s mobile
apps for Android, Blackberry, iPhone, and Windows Phone.
In the meantime, we’re hard at work on further improvements to the
MediaFire features that our users have most demanded. We’ll keep you
posted on new developments as we get closer to launching!
Source Shutting down MediaFire Desktop, new desktop app coming