For what it's worth...
As an FTE and a specialist in air data and navigation systems, I think I may have something to add to this debate.
Firstly, I have to agree with Ghengis; if the airmass is stable (in terms of temperature and density), a change in wind speed/direction WILL NOT change the relationship between CAS and TAS. Windshear could temporarily alter the values indicated in the cockpit due to its effect on the pitot and static systems, but I do not believe windshear is a factor in this discussion.
If the aircraft encountered a sudden change in wind speed/direction, that suggests to me that there may have been a change in other things as well, e.g. QNH, air temperature/density, and perhaps also the vertical component of the relative airflow. If the relationship between pressure height and temperature changes, the air density will change, and thus the relationship between CAS and TAS will also change.
Another thought is that the aircraft in question (being a GA aircraft) probably does not have an air data system that calculates TAS from total temperature; therefore the GPS based navigation system will be trying to derive TAS from the difference between TRK/GS and HDG/CAS using the triangle of velocities and GPS height. This is an error prone method because: 1) the system will have to make assumptions about the atmosphere, particularly the relationship between height and the air density; and 2) it will be trying to do the maths assuming a reasonably constant wind. Also, if the system does not have an airspeed (or heading) data feed, it will also have to make assumptions regarding HDG/CAS. Therefore it is unlikely that the TAS and W/V estimates will be particularly accurate. Typically in these GPS based GA nav systems the information on TAS, W/V, etc is there to help the pilot with situational awareness but is not going to be so accurate that it can be treated as gospel.
To my mind the ONLY way an air data system can get an accurate derivation of TAS is to have accurate and properly calibrated air data sensors (pitot, static and total temperature). If this data is used in conjunction with an accurate source of TRK/GS (e.g. GPS/EGI or INS), and an accurate source of heading (such as an INS or AHRS), then and only then can an accurate instantaneous W/V be calculated.
If someone provides me with exact details of the systems integration on the aircraft in question (particularly the air data and heading sources that feed the navigation system), I may be able to provide a more specific explanation of where the problem is likely to lie.
Hope this helps.
WF