When I write "My app" that means I wrote the app. I'm a software author so to me when you write "My gmail app" it does not mean you are using some app but something you wrote. Your app.
In case that was not true, try other email apps. Examples are plentiful and http://forums.androidcentral.com/android-apps/511945-whats-best-android-email-app-thunderbird-out-android.html kicked it around a bunch.
In my android phone when I refresh my default Gmail app it shows me no new message and every time I have to remove the account and add again. Is there any possible way to solve this issue?

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