A servo, if working properly, can only do as it is told by the receiver. This, in turn, only passes the message along that comes from the transmitter.
A servo getting no signal will twitch a bit on power-up, and sit there, twitching the same way at the next power-up, until it eventually gets to the end of its travel.
If it travels to the end in one go, it is getting a signal telling it to do that, and it begins to look like either the transmitter is sending an "out of range" instruction, or the receiver is translating its signal to something out of range. If waggling the stick does nothing, it could mean that the signal never gets to the point where the servo can respond.
Or there is something in the servo causing the problem. In my case, when something like that happens it is salty water where it shouldn't be altering the servo circuit.