It would be really useful if you could set different responses in STHM based upon stay or away modes (separate responses for each mode).
I’d settle for the app remembering my text recipients in the Set up response 
Every time I set up and save, I come back later and they are blank. So I only get push notifications.
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@jkp, I had that same STHM SMS Response saving issue back in February.
However, I was able to resolve it myself at the time. I uninstalled the latest version of the SmartThings Android app, and side-loaded the previous version at the time which was SmartThings version 1.7.40-21 for Android. The older version allowed the contacts I entered into the STHM Response feature to save. I even updated back to the latest version of the SmartThings app at the time, and my contacts were still showing in the Response section of the STHM.
As for different responses for either Armed Away or Armed Stay, I setup additional Automations to do that. And now that the Automations can run local, they are essentially a backup (or enhancement) of the STHM response.
My various STHM Automations trigger depending on my ‘location mode’ and not the mode of the STHM is in to make them run local.
‘If’ pre-condition my ‘location mode’ is in ‘Away’ which is when the STHM is in Armed Away, and when any condition is met from whatever sensor detection happens ‘Then’ trigger a response.
‘If’ pre-condition my ‘location mode’ is ‘Night’ which is when the STHM is in Armed Stay, and when any condition is met from whatever sensor detection happens ‘Then’ trigger a response.