The problem is in the master cylinder. The MC is in effect two cylinders in one, one cylinder for the front
brakes and one for the rear (one in front of the other). When the MC gets a bit long in the tooth pressure from one cylinder can leak past it's seal into the other cylinder or into the reseviour.
The MC is leaking internally, but not externally, so you see no signs of leakage and don't lose any fluid as leaked fluid ends up back in the reseviour. Sometimes the symptom will be evident and other times not, on my car the pedal tends to sink sometimes on hot days but is always firm on cooler days(?).
It really is something that does need to be addressed urgently as a matter of safety, because pressure is leaking from one cylinder the pressure in that cylinder won't be high enough. This will affect front to rear brake bias which can have a substantial adverse affect on braking
performance, and may cause premature brake lock up at either the front or rear (not sure which end), which could cause loss of control (i.e. massive understeer or oversteer under brakes).
$700 does sound at least a bit steep to supply and fit a new MC, and bleed the brakes. Here in Australia new Accord MCs are around AUD$180 or so.
The pedal should be quite firm with little free play with a braking system in good condition, if yours typically isn't (before you had that sinking feeling) then the brakes probably need attention (bleeding most likely, but could also be a soft rubber hose, causing the hose to bulge under pressure, not good as it may burst).
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