Yes.  The very first race I created I was able to save, and when I started a new game it was available to use.  However, I decided I wanted to change it, so I deleted it (via the in-game delete button) and the recreated it and saved it.  This time it didn't get saved, though, as you describe.  I've since started another game and created the same race over again (and saved it) but again I see nothing in the factions folder.

This seems like a bug, perhaps you should move this post to the Support forum by editing your original post and selecting "Support" from the drop down list under Categories, and then saving the post.

I had a similar issue what it looked like to me 

if i created a race

then went directly into a game as that race

then exited game without returning to main menu Or saving game

Then the race would not be in the race list

this is only my half remembered observations

Not sure if this is helpful or not, but I couldn't reproduce this error when I disabled sync with Steam cloud service. 

We are currently looking into this issue as a high priority. For anyone experiencing this issue, please submit a ticket if you have not already. Please take a look at the following article and provide the requested data in your ticket:

https://esupport.stardock.com/index.php?/default_import/Knowledgebase/Article/View/496/161/general-galactic-civilizations-iii-troubleshooting#support

I think you may be on to something, as Steam Cloud syncing was added in Beta 5... I'll forward that note to the development team, thank you! 

To add to this, I have Steam cloud sync disabled and have been able to make multiple races without issue.

I really appreciate everyone posting, this is a very high priority issue on our end. This seems like the type of case that any little detail would be very helpful in tracking down this issue.

List of the following details that may help:
Which options were changed in the custom factions screen?

Which images were changed?

Which fields were renamed?

Which racial traits and racial abilities were chosen?

Which appearance was chosen?

Which tech tree, personality, Ideology character traits and priorities were chosen?

Which Solar system was chosen?

What were the map options, galaxy type, opponents chosen when starting the new game? 

Do you have steam cloud saving enabled?

Is your steam account on multiple computers?(In reference to the cloud save trying to update on separate machines) 

My latest attempt worked, I now see a .faction file in my Factions folder.  The only difference between this and my previous attempts was that I had Steam cloud sync turned off.

For the record, on my last attempt that didn't work and with this most recent one that did work, I chose the following:

Leader: Changed the foreground and background pictures, the leader portrait, entered a leader name and simple description.

Race Overview: Entered a name, short name, ship callsign, homeworld name, and simple description.  Selected a race logo, chose Iridii as the star system.  Did not customize the start up screen.

Traits and abilities: Chose Patriotic and Prolific, Productive(1), Clever(2), Content(1), Fertile(1), Courageous(-1), and Fast(1).

Appearance: Chose Iconian ship style, made no other changes on this screen.

Personality: Took the default Basic Tech Tree, Pragmatic ideology, selected Peaceful and Spiritual character traits, did not change any priorities.

Large map, loose clusters, Altarian/Drengin/Krynn/Thalan opponents.

I have Steam on two computers, however the second one is 32 bit so I don't have GC3 installed on it.

I just tried creating the same race over again (from my last post) and it worked.  Took all the same choices.  This might be a red herring, a real long shot, but when I did it the first time, while entering information in the Race Overview window, I hit the tab key to try to advance to the next field (which it doesn't do).  I wonder if having a spurious tab in the race name causes the problem?

BTW, it would be nice it the tab key did advance to the next field.  With over 30 years experience entering data into forms on computers, hitting the tab key is a habit with me.

I also never hit the tab key when entering in race info... Lets do a test run to see if this holds. Yup, the race I made after hitting tab a bunch of times in the text portions did not save correctly.

Turkwise you are my hero!  Tabbing in the fields is exactly the issue. It's inserting an invalid character that can't be written out.  We will fix it! (not in time for this weeks patch, but in the next one).

Sorry I got excited and didn't see that you actually posted it first.  Bonus Karma to everyone!!!

And as a bonus we are going to get it into tomorrows patch!

Yep, Publius of NV it was your brilliant catch!  I just tested it.