There is a letter to elders on the subject of resigning, it was sent around maybe 4 years or so ago.
In the letter, mention was made of elders meeting with and 'speaking to' a brother who wished to resign. No specific mention is made, to my recollection, of trying to talk him out of it or not allowing it, but rather to discuss it, as one would expect.
I believe the letter then mentions that, if the brother still wants to resign, the matter should be held until the visit of the C.O. I cannot recall exactly what is stated next, but my guess is that they'd want the C.O.'s input.
It seems to be a more complicated process than one might expect. I remember sitting there when the letter was read among the elders thinking "geez, if a guy wants to quit, let him quit". I can see discussing his reasons with him, but I don't think that, per se, he is "not allowed" to resign. However, some of my recollection could be inaccurate. Also, there may be a portion in there about the elders' not accepting the resignation, and if so, that does just about amount to not being allowed to resign. But the fact is, I know personally of elders who did resign and there did not seem to be a fuss made. No elder ever quit from the body while I served though, so I am not sure exactly how the other resignations were handled.