This can happen if your app settings are balanced towards higher security, at the expense of convenience.
To unlock your database more quickly, please make sure that you have “Remember master keys” enabled, and Database Lock timeout set to sufficiently long value. The first one ensures that the master keys (password + key file) are kept for future re-use when you unlock the database. The second one erases stored keys after some time.
Also, to quickly switch between databases you should simply navigate back from the database (using the top-left button or left-to-right swipe gesture across the screen). This keeps the remembered master key. In contrast, the lock icon at the bottom erases the remembered key, and you would have to enter the password again.