In the examples you give without a pronoun, the possession is implied; there is only one mind that the subject of the clause can keep anything in, or have anything come to. There is also the possibility of usage where the statement refers to minds in general, and uses "mind" without a possessive pronoun to indicate that it is true of any mind, as in "A mind all logic is like a knife all blade."
edit: in response to user3738870's comment:
I admit I do not know of any specific grammar rule dictating when it can and cannot be implied. My only theory is that, as you implied, all the phrases where it is implied are somewhat idiomatic; they are common phrases whose meaning is not perfectly clear from the meaning of the individual rules (I would consider your third example to be an idiom as well, although a less common one). Phrases like this often follow outdated rules or break the rules entirely; I assume this is the reason it is only natural in specific circumstances.