riddle - Enjoying a rest from the long commute!

You ask me where I used to work before I was retired?

Perhaps you’ll know if I tell tales of workers that I’ve fired...

The first who came and worked with me was fresh from Ivy League,
But at twenty-two her labours brought her burn-out and fatigue.
The second one could rival her, just as strong and smart,
But one day pushed herself too hard and sadly fell apart.
All five of them were brilliant, but the third achieved the most;
Truly ‘quite the find’ when we first advertised her post.
Yet she never clicked with Number Four – they just did not get on;
Though Four was still a legend, making sure the work got done.
And Number Five – what can I say? She always tried her best;

Enterprising, striving hard – I always was impressed.
In fact, we had eight happy years with only Five, Four, Three;
But in the end the project closed, they took redundancy.

So hopefully my little rhyme resolves your question – does it?
I had a job for thirty years, so tell me now: Where was it?

Answer

So, going in the thread of @AndrewSmith's answer, I'm going to fully answer the question here:

You worked at:

NASA

The first who came and worked with me was fresh from Ivy League,
But at twenty-two her labours brought her burn-out and fatigue.

Columbia is an Ivy League university. The space shuttle Columbia served 22 years before disintegration during re-entry.

The second one could rival her, just as strong and smart,
But one day pushed herself too hard and sadly fell apart.

If you challenge yourself, you push yourself to your limits. Challenger was destroyed in a mission accident in 1986.

All five of them were brilliant, but the third achieved the most;
Truly ‘quite the find’ when we first advertised her post.

If you find something nice, you could say that you made a great Discovery. Of all the Space Shuttles, Discovery made the most flights at 39 flights total.

Yet she never clicked with Number Four – they just did not get on;
Though Four was still a legend, making sure the work got done.

Atlantis is a legendary sunken island. Edit: just got the joke! Atlantis never got on with Discovery, because we never actually discovered Atlantis (the island)!

And Number Five – what can I say? She always tried her best;
Enterprising, striving hard – I always was impressed.

This could either be Enterprise, the test shuttle (for a literal meaning of "enterprising"), or Endeavor, which is closer to the overall meaning of "striving hard" and being resourceful. I'm opting for the second of the two, Endeavor.

In fact, we had eight happy years with only Five, Four, Three;
But in the end the project closed, they took redundancy.

From 2004 to 2011, the last 3 space shuttles were the only ones operational. After that, the Space Shuttle program came to a close.

Title:
Enjoying a rest from the long commute!

Going to space and back is a very long commute.