With an external monitor plugged in, I鈥檝e noticed that the session on the external screen hangs/is unresponsive, after the iPad screen goes to sleep and is woken up again.
Ctrl-^ .I'm having a similar issue on the same system, iOS 13.4 17E255 and Blink v13.3.219
@b00giZm did you connect your display after you opened Blink or before?
If I open Blink with display already connected, the external display is stuck on a white "Locked" screen and never recovers. Cmd + O moves the white "Locked" display to a split-view on the main iPad screen.
If I open first and then connect a display, things work until I switch away to another app, and then switch back (after which the external screen is unresponsive as above)
Sometimes when re-opening, the iPad resprings.

I have this same issue after switching applications from and back to Blink. Does seem to be a minimum time away needed to replicate, it doesn鈥檛 happen during a quick switch.
The session on the iPad screen immediately picks up and is responsive, but the external monitor session is not responsive after a Cmd + o to switch to it.
As a workaround I found that creating and closing a new tab (Cmd + t followed by Cmd + w) on the external monitor reactivated the terminal session on the external monitor.
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I have this same issue after switching applications from and back to Blink. Does seem to be a minimum time away needed to replicate, it doesn鈥檛 happen during a quick switch.
The session on the iPad screen immediately picks up and is responsive, but the external monitor session is not responsive after a Cmd + o to switch to it.
As a workaround I found that creating and closing a new tab (Cmd + t followed by Cmd + w) on the external monitor reactivated the terminal session on the external monitor.