Why is IE8 still around? Microsoft, of all companies, has tried to support legacy software for as long as possible, and often longer than possible, by reversing EOL'd announcements. The fact you can still run most 10+ year old software on a modern OS from Microsoft illustrates this.
Look where Microsoft is today, I certainly don't wonder why that is.
Corporations define policies and procedures for software releases internally. They find what is stable, slap a stamp of infinity approval on it, and forget about it. If this is to continue, there will be an IE6 problem again in a few years, only this time it will be FireFox that is being blamed.
Browsers need to be updated often, this is only going to become more important as the web advances. If this breaks your stuff, if your intranet falls apart as a result, more than likely, this is the fault of your intranet, not that of the vendor software. If it is the vendor software, in a few days, a patch will auto update.
As a corporation, you can chose to fix your intranet, put in the time and money to repair your mistakes, or not. Doing so will benefit you moving forward, and eventually, your intranet will be modern enough that these issues will be no more than a small inconvenience. It is not the problem of a browser vendor to stagnate their software because you want to allow your own software to stagnate.
The source is available, you have options. You can fork your own, keep the software where you want it, and patch it internally. If you don't like that option, contribute back to the current version, and help move things along. If you don't like that, write a check to someone to do this for you. I would bet that Firefox will be more than happy to backport for the right price.
You don't get to have your cake and eat it too, especially at the expense of the rest of the internet using world.
All the suggestions in the comments of the linked article lean on FireFox developing different versions and augmented policies to somehow continue to support an old version to aid in keeping crappy intranet's working. Why should FireFox spend a moments thought on making a Corporate Legacy Infinity Support Humping Along version just to appease the corporations inability to progress.
Sure, it is a lot of work to roll out 500,000 updates to FireFox. Move to Chrome and that won't be an issue, you are always up to date. Or, maybe there is an auto-update mechanism to FireFox for that scale. But doing that, removes the need for a large staff to take months to years to plan a browser update. That sentence is so insane, having a team to plan and document the upgrade of a browser!
People will find small portions of their jobs are irrelevant. Progress is like that. One day, many of our jobs will be replaced by robots. There must have been resistance to the copy machine, and all those secretaries no longer had to hand type a letter from the boss. Carbon copy paper may have had equal resistance. Progress happens, sometimes at the expense of jobs. Stay on top of your industry, and change with it, and your job should be secure. Don't get comfortable with the fact that your job is hanging on by a thin thread of aged policy in a corporate environment that changes slowly. That will be forced to change, as we are seeing now.
Corporate IT workers are demanding to turn FireFox into the IE6 problem. This has come at the expense of the entire internet using public in the past. FireFox is not willing to allow that to happen.
Version numbers are going to stop mattering. When you check the version number in the future, it will say "current" or "needs updating". Embrace this, and your intranet will be modern and more bulletproof. Don't, and I hope you are confident there are other aspects of your business that do not rely on technology so you will still be relevant in some other field. Someone will always need to put more paper in the copy machine, maybe you can create a procedure for making sure that all the copy machines waste a page per print. Your job is safe for at least your lifetime.