If requirements define what the solution the solution needs to be able to do in order to achieve project objectives, and system specifications define how the solution will work from a systems perspective, then it follows that the system specification must be directly associated to the requirements that deliver the objectives.
So to answer your question, the secario that is most likely to produce "critical requirement failure" must be the when where the "the systejm specifiaction [is] disassociated from the business objectives".
Logical analysis or trial and error (also known as "evolutionary" or "emergent design") are two methods of solutions definition. Business Analysis should be about analysis (you would think from the name) and not about any techniques that do not involve analysis.
Analysis has a definition ("breaking a complex down in to its component parts in order to examin the inter-relationships between them" paraphrased from Merriam Webster and OED) and activities which don't do this should not be called analysis.
The component parts Business Analysts break projects down to are
- functional and non-functional requirements
- scope statements
- process rules
- data rules
We have a plethora of methodologies and CASE tools that do this.Too many as we really should only need one methodology for what is one set of components!
"Emergent requirements" and "emergent design" do not take this route - which has advantages and disadvantages - but it is not analysis.
There is a size issue here: to change the size of an input field on a single screen in all liklihood will not benefit from doing analysis on the change - you might as well just do it and see what the users think and change again if needed. At the other extreme a national database of information that supports Identity Card functionality should not be developed using "emergent design" - it is just too problematic and costly (as you alluded too in another post).
Between these 2 extremes there are the range of 'normal' or 'most common' sized projects. At what size does a project no longer become suited to "emergent design"? How would that size be measured?
I don't know - but if in doubt, I would recommend analysis as it is simply more likely for things to go wrong than right and Business Analysis minimises the liklihood of things going wrong.