Does Firefox cache submitted form content anywhere I can recover?

Don't change anything in that tab. Hit forward to get back to the connection error page, fix the network problem, and hit "Try Again". This will submit the original post.

For the benefit of whom has had trouble in finding the path in the Firefox UI, in this answer I'll try to detail the operation suggested by user "sh1" step by step, which in my case led to a succesful recovery.

First, stay on the "time out warning / error" page you saw before when you unsuccesfully hit the submit button, without attempting other interactions with the web site. Maybe not strictly necessary, but safer indeed (need more experiments to clarify).

Disclaimer: I'm using the italian localization of Firefox, so I'm not sure about correct translation of some of the commands further detailed. Anyway the steps were:

• As told by user "sh1", through the "tools" ("strumenti") menu, enter the "network" ("rete") section of the "web development tools" ("strumenti di sviuppo web").
• Right click in the empty area of the web development tools window and select "start performance analysis" ("inizia analisi prestazioni"); FF will offer you to retransmit the same data actually sent before the problem (for now, sorry, I'm not sure if this is the same course of actions triggered by simply reloading the page from here).
• Obviously at this point you will still be stuck with the error page, but this time Firefox has kept track of any data it has tried to resend; you will see a list of requests and the page elements pulled from the server.
• At the top of the list, select the POST request by left-clicking it; the window will split
• In the right pane, click the "Edit and resend" button ("Modifica e reinvia"); this will show another view, in which...
• ...In the "request body" ("corpo della richiesta") frame, you will find, interspersed with only a few MIME headers, your precious submission in copyable plain text :)

I was succesful in recovering form data by using those Firefox built in tools alone. Aside this, and for speculation sake only, in my case core dump was not feasible. That's because I haven't altered the appropriate static system defaults (which are to be set beforehand; see http://bencane.com/2011/09/22/kill-creating-a-core-dump/ ; in the distro I'm using this time - latest Xubuntu - the default setting mix seems to be "no core dump").

Cheers

Extending on Schwern's answer, because in my case I'm unable to fix the fault:

Go forward to the failure screen again. In the menus selected Web Developer, Network, and then the 'Headers' tab, and hit the 'resend' button.

This should show you a form (so you can hack around with it) containing your lost content. It may not be in the most convenient format, but at least it's there.

Works for me, at least. I was actually sat here with the dreaded "your post fell down a hole" screen, and when I hit "back" I went back to some javascript which reset the form to blank (thanks Javascript!).

It's important to note that going forward means hitting the button next to the Back button. If you've gone back to the form and found your content lost, don't touch anything on the page which might try to send the newly-emptied content, because then your only choice will be rifling through the core dump but without any guarantee of success.