Is the Eames LAX still made?  

No
Lounge height bases are not currently produced.

Any idea when they stopped...
Any idea when they stopped producing them. From what I see of LAX bases, they are quite rare.

they come on ebay...
...every so often. Both X type and H type low lounge LAX's show up occasionally in "base only" sales.
They are indeed less common, but not extremely rare. They can still be had at a somewhat reasonable price, depending on condition.
(not to be confused with the earliest 1st version and super low LAX, which IS harder to find in good condition with no breaks or repairs)
I have no clue when they stopped production on the low lounge H with plastic glides. (But the earlier X version probably transitioned into the H around 57 ish like the dining bases)

Production ended a long while ago. . .
I have quite a few of them and have sold one or two over the years. Find it odd that there isn't a bigger interest in them. Easily one of the more comfortable bases for your retrotastic, Mad Menesque Eames chair. Hooray!
EDIT: Edited once again due to this "dot dot dot" fiasco.

I know the LAX you are...
I know the LAX you are talking about @EamesHead. Something like this... http://krrb.com/posts/29598-charles-eames-lax-1st-production-chair

Crashdesk
I think that is the "normal" early version LAX low lounge base. There is one even before that. The seller says "1st year", and is probably referring also to the rope shell itself. The legs look thinner than the later ones, as they should, but too tall to be the earliest ultra low 1st version. Photos make it difficult to tell sometimes, especially with these bases, so who knows?
To my knowledge there are actually three versions of the low LAX before the H:
1) The earliest UBER low X- (I think "Moddesigner" on ebay has one for sale)
2) The slightly higher "low X" (still with the thin metal legs and domes glides)
3) The highest, last "LOW X" ( with boot glides, and made until the Low H with
metal glides in '56
LUNCHBOX ... (notice those dots?) I agree about the Low H Base. It is weird that they are not more in demand. They are beautiful and very comfortable. I enjoy still being able to snag one cheap on ebay now and then. Eames shells simply look better on a low lounge most of the time. Be it aluminum or in black. Sometimes its nice when the things one covets are not horribly expensive! (Yet?)
I am still looking for a black low H lounge with the "56" metal glides. Prettiest h base on the planet! All the better if it is solid and not tubular, to match my one and only...

Cheers Eameshead. How cheap...
Cheers Eameshead. How cheap is cheap? 🙂

cheap is...
I recently bought a nice pair of low H bases on ebay for 50 bucks, but that was the best price i have seen in some time... usually they are 40 - 60 ish for one. Still cheap in my opinion. I've seen them with higher asking prices but they tend to sit a bit at the higher prices.
Some sellers don't seem to differentiate between the low H and the higher H bases that they have left over after selling their shells separately.
Some sellers don't even seem to know that they are selling a low H. I think there is an assumption that everybody wants reproduction rocker bases, or eiffel bases and the H bases get lumped together.
I would rather have a vintage original low H than a fake anything else.