I ran into the same issue when I first got my hub a month ago. It was only resolved once I upgraded my phone to marshmallow. I had tried everything from reinstalling the app to wiping cache to factory resetting the phone.
Try the following
Close the app, and go wipe app data and cache
Ensure that in android app settings show notifications is enabled
If that doesn’t work you might have to try a reinstall, then before opening the app do steps 1 and 2.
I found when I enabled it I had to set up my account to allow push notifications. Its nice cause I can control who gets notifications a little better.
So it does look like its is sending just something not working. Zebrablind step 1 and 2 are good steps, but before going crazy and factory reseting phone I would contact support. There may be a blocked queue so messages are not being sent.
To check notification settings go under Settings->App->SmartThings->Notifications
I noticed ST is not set for priority notifications. Double check your phone that it is not set on Do Not Disturb.
I figured out why my app stopped processing notifications. I had wiped the cache for the app in an attempt to fix the overall slowness I am finding this device is causing on my HTC One M7 based on a recommendation to do this posted to my other thread about poor android performance when ST is installed. It seems like deleting the cache caused my notifications to stop working. I am surprised by this because you should be able to clear a cache and not affect an app but this seems to have been the cause.
I uninstalled and re-installed the ST app and the issue has gone away.