So in each Proof-of-Stake blockchain, there might be only a limited number of these Master Nodes?
POS was not always using masternode. As someone said above as there was no limitation but that depends on how good the profit margin when you are become the masternode. People will not use a lot of money to be a masternode if that was not even profitable.
But what will happen if one of these Master Nodes run into errors and you do not have an alternative Master Node right away?
that's why the masternode coin will have another option like it will let miners to help to secure the network too. In masternode service and what means of POS is proof of service and it's not proof of stake.