Login session ends immediately in Firefox, but works fine in Chrome.

The first thing that comes to mind is: Cookies

You have already checked your cookies; but, have you confirmed that they are not damaged?

Besides cookies, here are some reasons why this happens:

(a) The date on your computer is not set correctly. Since cookies are date-specific, a computer with an incorrect date can mislead your browser into forgetting about your cookie. To fix this, set the correct time and date on your computer.

(b) You have installed an application that controls / blocks the sending of cookies. It could be antivirus software. To fix this, simply disable the monitoring application before logging in.

(c) You are behind a firewall that does not allow the receipt of cookies. This sometimes happens for users connecting from a business intranet who restrict cookie acceptance for security reasons.

(d) Your browser is simply not configured to accept cookies (although I think you've already checked that, right?)

(e) Your browser cookies are corrupted. (This is what you may have missed)

(f) Your browser itself is damaged. (Not sure how to fix this, but you can try to completely remove it from your system and then reinstall it)

Here's another solution that might help you:

(a) Start Firefox in Safe Mode to check if one of the extensions (Firefox / Tools> Add-ons> Extensions) is causing hardware acceleration;

(b) Switch to the DEFAULT theme: Firefox / Tools> Add-ons>. Firefox uses the about: protocol to access embedded files: pages that can be opened through the location bar in the same way you open web pages.

(c) DO NOT press the Reset button on the Safe Mode start screen or otherwise make changes.

(d) Delete cookies. If clearing cookies doesn't work, it is possible that the cookie.sqlite that stores the cookies is corrupted.

(e) Rename (or delete) cookie.sqlite (cookies.sqlite.old) and delete other existing cookies such as cookie.sqlite-journal in the Firefox profile folder if cookie.sqlite is corrupted.