Maester Munkun - What is his deal?

[Floki of the Ironborn]

On the one hand, Munkun seems to be a wise man. He mediates to keep the peace, he is the first on hand to try and heal people, and he occasionally gives some genuinely sound advice (ex. suggesting Rowley to be the new Lord Confessor). On the other hand, he spends years actively assisting and supporting Unwin Peake, even to the point where he's disobeying Aegon's orders. Of course, Munkun's status means he doesn't get punished with the others, but something must have happened because he apparently gets dismissed from his position by the time future Daeron II is born. But then later on he's in the same position as before. Is that a blooper on GRRM's part? Did Aegon and Viserys punish him for conspiring against them after all? 

[Alester Florent]

I suspect he just sucks up to whoever needs sucking up to at any given time and tells their successors that he didn't want to go along with anything they did, etc. In any case, he's a maester and they're supposed to advise the position, not the man. So the Grand Maester isn't expected to be hired and fired in the same way as the rest of the small council bods.

Pycelle saw out a number of radical shifts in direction and ruler before Varys killed him. He served four kings as Grand Maester, many more Hands, and the only person to try sacking him in all that time was Tyrion, who fairly quickly found that decision undone. I would imagine Munkun played his cards similarly.