Telepathic hint to join in received from JT!
To get a handle on this discussion, I think that it's important to start by appreciating that longitudinal static stability has a large number of flavours, the main five being:
Aerodynamic stick free
Aerodynamic stick fixed
Apparent stick free
Apparent stick fixed
Manoeuvre stability
These are all linked, but separate.
The first two are what the aerodynamics textbooks talk about when they consider LSS but from pilots perspective they aren't all that important because designers have lots of mechanisms to transform those aerodynamic characteristics into different apparent characteristics
The characteristic which (rightly in my opinion) is the main concern of all of the certification codes is apparent stick free longitudinal static stability. This is measured by stick force per airspeed change. It's important for the simple reason that pilots perceive control forces much more than they do control positions, and really couldn't care less about aerodynamics so long as it's all sorted out by the time it reaches the cockpit.
There are various bits of guidance out there as to what is an acceptable gradient for aLSS; for example a well known textbook by a chap called Jan Roskam recommends a minimum of 6kn/lb; and when I have in the past been involved in certifying light training aeroplanes I had a personal working minimum of 0.1 daN/kn, which comes out pretty much at Roskam's number if you convert it. Most transport aeroplanes are likely to want a higher gradient than that but, it's important to remember, this is only what is perceived at the cockpit.
However, the designer and airline accountant have other views on aerodynamic stability. In simplistic terms, at forward CG the tailplane is providing a downforce and the further aft you move CG, the less that force is. That force pushes performance down and fuel burn up, so it's a bad thing (to airline accountants) so there will always be pressure to move it back. A CG of around 40%MAC (as mentioned by ALK A343) will give a neutral to slightly negative aerodynamic LSS; such an aircraft is flyable aerodynamically even without stability augmentation (not a heavy, but most of us have flown a C150 at some point - at mid-aft or aft CG, 30+ flaps, 65%+ power, that is statically unstable, but some very low ability pilots manage to fly go-arounds in it safely). However, the modern designer will provide a Stability Augmentation System (SAS) to modify that in a large aircraft so that by the time the pilot sees the longstab, an unstable aerodynamic longstab which would be unpleasant and push workload up, has become "just another airbus".
All this is done in the name of efficiency - you could push the CG forward, not bother with the SAS, and have a flyable, but less efficient aircraft.
Having said that, part 25 contains requirements that in the event of loss of a single axis of primary aerodynamic control, the aircraft must still be controllable. For most airliners, the design philosophy this forces is that in the event of an elevator / stabilator control failure, the aircraft is designed to be flyable on the pitch trimmer - not a lot of fun, but doable. This is doable by ensuring that the aircraft remains flyable (just!), by not allowing aerodynamic stability to become too negative. - hence an aft limit of around 40%, rather than (say) 50).
Stick force per g (what I've referred to above as manoeuvre stability) is a bit of a red-herring here. It's a related but separate entity. Essentially it's a function of how much pull is needed to pull how much g - that little bit of back pressure that we all know we need to apply in a level turn for example. Airworthiness standards since the 1950s have pretty much all required the same - that you have to pull at-least 15lbf to reach the positive g limit. This requirement is generally a trivial one since most aircraft in any class, which have acceptable LSS, will comfortably exceed this requirement. We were entertained the other day by discovering a research aircraft flying at a weight of about 37 tonnes flying 2g turns, started to display neutralish manoeuvre stability, as result of which 12 scientists up the back all got treated to 2.4g - but that's my problem!).
G