Saving a keiki with no roots from dying stem

[pixie.devries]

Hello! I am new to the orchid world and learning how to care for one given to me. I'm not sure of the species. The issue I have is that I have 2 stems with each now growing beautiful little keikis.

This last week one of the stems started dying and it is now down to where the keiki is and it hasn't started to root yet. What can I do to save it?

My other keiki only has 1 root growing and is about 2.5 inches long. How long can I expect to wait before seeing oter root growth?

I appreciate any and all help! Thanks in advance

Pixie