Welcome to the forum!
What equipment are you using besides the blu-ray player and the screen? Do you have the player connected through a receiver?
Also, after you watch a blu-ray, what do you do? Do you switch to another source, like a cable box?
If you are using an HDMI connection, then it sounds like a handshake issue - but I've never heard about it taking that long to reconnect. My system takes maybe five seconds to switch between HDMI sources using my receiver (it's faster when switching between HDMI sources on my TV).