Indeed, I experimented a bit with an Android 2.3.6 device and managed to reproduce similar behavior. Basically, this appears to be connected to timeout errors in the WebView. This is easily observable if you connect your device to the Android Device Monitor
In order to fix this behavior on my side I used the following preference in the Android Config.xml
file in my AppBuilder project.
Also, make sure that you are loading the Everlive JS SDK from a local resource and not from a CDN.
Also, in order to handle push notifications in the background of the app, you need to modify this line
of code in the Telerik Push Notifications plugin and import the plugin manually from the GitHub-exported ZIP arhcive.
To illustrate the working behavior, I prepared a simple example which you can clone in AppBuilder from here
Prior to testing make sure to populate the API key and the Google Project Number in the app and deploy as an app package to a device.
Samsung Nexus S
Backend Services JS SDK 1.3.1
Push Notifications plugin 2.5.7
Let me know if this helps.