When using an iPad with my Perspective project, I noticed that if I used either of the dropdown selectors for month or year in the datetime input, I wouldn’t be able to dismiss the calendar popup.
Typically, I tap the input to get the calendar popup and tap off the component to dismiss it. I would expect this to work the same after using a dropdown on the calendar popup, but the first tap off dismisses the dropdown list and any number of taps following just leave the calendar popup in place. However, if you use the arrow buttons to toggle the month, then you can tap off to dismiss the popup again. Throughout you can select a date to dismiss it as well (unless you have dismissOnSelect set to false, as I did).
You should be able to reproduce this by dragging the generic datetime input component onto a page and using it on an iPad as described above.
I didn’t see this issue on an iPhone or on desktop - seems like a very specific (and minor) issue for the iPad.
7th gen iPad on software version 15.1, project open in Safari
Ignition 8.1.12 Perspective