Silas, I tried uninstalling and re-downloading then re-entering my username, password etc. While inside the LAN and using wifi I confirmed that the iOS app was able to connect to the server. I then turned off wifi and using only the cell connection tried to connect to the server and failed.
Fenderman, I'm not sure which settings you suggest are wrong but on the iPhone the following are set for
Blue Iris:
use cellular data; allow notifications; show in Notification center (these come through, by the way, even though I can't connect to the server); sounds; and background App refresh is turned on.
To recap: everything used to work, until a power glitch at the house caused the DSL router to go off. When power was restored, of course the external IP address changed (because I don't have a static one). Blue Iris on the PC in the house knows about the new external IP address, and when I'm within the LAN using Blue Iris on my iPhone, it also knows about the new external IP address.
What else might I try?