I downloaded the splash screen example from the Xamarin website:
http://developer.xamarin.com/guides/android/user_interface/creating_a_splash_screen/

I compiled it and ran it on my phone:
http://www.gsmarena.com/samsung_galaxy_fresh_s7390-5841.php

It was working fine when holding my phone in portrait mode (vertical). The splash screen became directly visible and after a few seconds, the view with the button became visible. When closing and restarting the application, it was still working fine.

After that, I closed it again and hold my phone in landscape (horizontal) mode. Now, I started the application again. My phone was frozen for a few seconds, the splash did not become visible. After that, I saw my view with the button.

When you try to reproduce this issue, make sure that you:
-do not try to reproduce it on a tablet (at least on my tablet this issue does not exist).
-do not try to reproduce it on a virtual device (the behavior is different).
-make sure that the sleep takes at least 10 seconds, then you really see what the problem is: a frozen application instead of a splash screen.
-If you do not have the Samsung Trend Lite, you try it on another small smart phone. I find it hard to imagine that this could be a "Samsung Trend Lite only" issue.