I can get into the playstation store no problem when I turn on my playstation 4. But if I open a game and quit out of the game, the playstation store fails to work afterwards. It'll just put me into the loading screen and the only way I can get back is quitting the application. This has happened since day 1 for me.
Sounds like a possible local bandwidth issue if you are suspending your gameplay or app rather than shutting down programs completely