5th dnd – What happens to concentration spells by flashing?

I see regularly wink praised as a particularly good third-level defense spell because, unlike many persistent-effect spells, it does not require concentration. However, it is stated that "you can only affect and be affected by other creatures of the Material Plane".

I do not know exactly what this means for the concentration spells cast before the thrower starts to blink. So, here are some specific questions:

  • If I throw hold the person so what blink, is the target still affected by hold the person while I am on the ethereal plane? (I think the answer is no.)
  • Targets can save money hold the person at the end of their turn. If the answer to the previous question is no, can the target save while she is not technically affected by the spell? (I think the answer is no, but it seems to be entering a strange territory, because they can save only if I do not blink?)