I am familiar with HDOP and GPS usage in general (previous UAV Pilot for the military and current UAV support specialist.) The issue is simple. With 12 satellites locked and an HDOP of 1 or less is not a condition that should set off a "Searching for GPS" warning simply because the satellite count went down by one or two. In all other systems I use this type of warning is used for when the PDOP is more than a preset limit.
Simply put, a GPS warning should be reserved for when you are in danger of losing GPS assisted navigation, which is definitely not the case when going from 18 sats to 12 and a HDOP from .6 to 1.
I think that the system is claiming to see or track 10 sats, but not claiming to be using all 10 sats for the fix. (My limited understanding is that "fixed" is a threshold parameter that has to do with the firmware of the receiver.) So, a receiver could be tracking 10 sats, but only using 4 in the position solution. (I believe 4 is the theoretical threshold, but that would provide no checks, so there would be no way to establish a "fix" status. Thus the need for 6, or more.) If you want to get even more complex, think on this, most receivers track dozens (high end hundreds) of channels. This is because each SV transmission results in multiple paths to the receiver, and a high end receiver will track many of them, rejecting the ones that are the result of multipath.
DOP (GDOP, HDOP, VDOP) is NOT an assessment of the quality of the GPS fix. That seems to be a HUGE misunderstanding. The last time anyone had a truly bad DOP anywhere in the USA was probably 2002, unless they were in a canyon. DOP is a THEORETICAL assessment of the figure. Think a right angle triangle vs an oblique triangle...one is a strong figure, one is a week figure. That is what DOP is assessing.
A good receiver is constantly assessing and adding and eliminating sats from its solution, and using various means to determine whether the solution falls within the parameters needed for a fix.
If the receiver says, "no good", Solo has a go/no-go communication, but that decision is made by the Ublox engineers, Solo is just telling you the news. There is no warning that you are going to lose GPS assist, just a indication that it has already happened (past tense).
In the systems I use for work, there is a constant update of the HRMS and VRMS, and then there is a "fix" designation that is essentially an assessment on if the HRMS and VRMS estimates can be trusted. There is also communication about the number of visible sats, and the number being used in the current solution. If I want, I can look in a sky view, and see where each sat it is using is located. Then, I get to choose whether or not to trust the position solution. That would be unwieldy in a quadcopter, I think, and likely beyond the average consumer's desire to understand.