The second flipper only frees up the flipper because of the vibration it creates.
With the flipper stuck up, take your fist and pound it down on the middle of the wooden playfield. The stuck flipper will drop.
Given the circumstances you provided, there is nothing “electrical” that could hold any coil in the up position, beyond the grounding switch itself.
All coils always have power. The thing that makes them fire is actually them being grounded.
In the case of a flipper on a black Pryamid, when the flipper coil is grounded, the flipper coil is fired and the EOS opens, simply increases the resistance in the circuit so that the coil does not burn up.
Based on your symptoms, the flipper switch on the inside of the cabinet could be arcing and heating up fast enough to weld itself shut.
HOWEVER, 99% of the time, you are going to be looking for a physical problem with the flipper actuating once and remaining up.
Like, the spring, the plunger, the sleeve, or not enough lash on the flipper shaft.