This is almost certainly caused by an extension. If you use Firefox with few or no extensions (e.g. 1Password doesn't cause problems) you'll find this doesn't happen.
Although badly-written extensions do cause a lot of problems, please don't assume they cause every problem. It's not always true and comments like these give the impression that Firefox developers simply pass the buck every time somebody complains.
Having said that, if someone is experiencing bad performance and they do have extensions enabled, temporarily disabling them is a good diagnostic step. If performance improves, it's clear that it's an extension at fault, and then bisection can be used to work out which one. Otherwise, it's clearly a Firefox problem and a bug report (bugzilla.mozilla.org) would be very helpful!
Isolating a problem is always a good idea – but scope is also a factor: the original claim that Firefox becomes slow simply from normal usage would require everyone at Mozilla not to have noticed during a multi-year performance push. I've never worked there but that seems unlikely.
Pretty much. I never close Firefox on my laptop, and haven't seen any performance degradation for over a year now.
Chrome on the other side, starts degrading my entire system's performance forcing it to hit swap memory the second the string of tabs on my top bar threatens to stretch across the screen. No need to wait for 'months of use without closing'...
