“in any event back button is close the app”
Its obvios why the application is closing all the time.
{
this.rootPage=Welcome;
this.platformbegin(); //<- !
}
You are initializing the function when the app is starting.
Resulting in = App closes because of: this.platform.exitApp();
[The problem could be that your counter is NOT working and it just runs the else code! Maybe adding a console.log would show if the counter is really working or not.]
this.platform.registerBackButtonAction(() => {
if (this.counter == 0) {
this.counter++;
this.presentToast();
setTimeout(() => { this.counter = 0 }, 2000)
} else {
// console.log("exitapp");
this.platform.exitApp();
}
}, 0)
Bind this code somewhere in your typescript but not in the initialized function.
(Idk if your counter is working or not Im asuming it works for now, but I see a mistake in here.)
Simply add an else if.
this.platform.registerBackButtonAction(() => {
if (this.counter == 0) {
this.counter++;
this.presentToast();
setTimeout(() => { this.counter = 0 }, 2000)
} else if(this.counter == 2){
// console.log("exitapp");
this.platform.exitApp();
}
}, 0)
Im also not sure why this: 0) is present in the end of your codeline.
You also should be able to initialize it again with your function with this code.
If that doesn’t work. You might just add a Backbutton in the HTML yourself and create a function for it and bind this code to it just without this.platform.registerBackButtonAction(() => {
I hope this helps you out a bit. 
