How can the F-16 remain stable when there is a loss of hydraulic power?
As I understand it (I'm neither an F-16 pilot nor an F-16 mechanic), Relaxed Static Stability doesn't mean the aircraft is unstable, just that it's less stable than the long-established standard.

To put it another way, if you build a free flight model airplane scaled from an F-16, you'll have to put the center of mass significantly further forward than its location in the full size, piloted F-16, in order for the model to have static stability.  The same is true of many radio control models intended to be flown by an experience model pilot -- they're what's call "neutrally stable".  The primary characteristic here is that these models will "go where you point them" and require that you "fly them all the time" -- unlike a trainer, or many/most scale models of piloted aircraft, you can't just set the throttle to cruise and take your eyes off the airplane, and expect to find it in a predictable location a minute later.

The same is (mostly) true of the F-16, in that, in most flight regimes, it's stable enough that as long as a violent maneuver wasn't in process when the flight computer restarts, the aircraft won't be badly out of shape by the time the computer returns to full function.  Back in the 1980s, however, it wasn't unheard of for a pilot to have to eject due to a fly-by-wire system failure; my parents lived near Hill AFB and would hear by local rumor mill and newspaper of "another F-16 crash" every so often.

Bottom line (again, based on my understanding as an "interested bystander") is that the F-16 is just about stable enough that it can remain recoverable through a control system restart, if it was in a steady state flight condition beforehand.