The endplate at the NMJ doesn't fire action potentials. It has Nm channels, which permit depolarization, which then spreads along the endplate to the adjacent sarcolemma that does have fast Na channels and hence is capable of firing APs (and hence contracting muscle). To be successful, the endplate depolarization (which will decay with distance) has to be greater than the threshold once it reaches the sarcolemma.
Succinylcholine is two ACh molecules joined together, so it initially activates the Nm channels and leads to the cascade that causes muscle contraction. The problem is that while ACh is removed from the Nm channels by acetylcholinesterase, succinylcholine is resistant to its action. To create another endplate depolarization (and hence another AP in the adjacent sarcolemma, and hence further muscle contraction), the endplate has to be repolarized back to its RMP first. This is normally accomplished by acetylcholinesterase degrading the ACh thats activating the Nm channels...which is something succinylcholine is impervious to. Hence it remains attached to the Nm channels, producing a persistent state of depolarization. This means the fast Na channels in the adjacent sarcolemma will be stuck in a voltage inactivated state, unable to recover to the resting state (this is similar to voltage inactivation of fast Na channels in ischemic myocardium).
The above is phase I. SCh initially depolarizes, which causes fasciculations. Continued depolarization essentially means the sarcolemma cant fire APs due to voltage inactivated Na channels --> flaccid paralysis. Since ACh has the exact same action as SCh, acetylcholinesterase inhibitors in phase I will worsen the issue.
Phase II occurs when the Nm channels get desensitized to SCh, which then dissociates. Obviously this allows the endplate to repolarize, which means the sarcolemma regains the ability to fire APs (Na channels recover from the inactivate to the resting state). The problem is that since succinylcholine is essentially two ACh molecules stuck together, desensitization to the former also means desensitization to the latter. Hence acetylcholinesterase inhibitors might or might not be able to reverse phase II.
