With the recent halving of block rewards, the incentive will be lower than previous for miner. On the other hand, the cost for them will still be same which may not be profitable for a while (I'm not sure about this). If it is true, is it possible that some miners will just leave mining for a while until they get back in a equilibrium or in profit? What fo you think?
It is very possible and it has been happening.
The cost may rise or fall. The main cost there is the regular or non-stop electricity that miners need. But that is not something they cannot do anything about. They have certain options to counter it. But as to whether they will continue surviving with a profit despite the just implemented inflation of rewards, they will see in the next month or two.