@BLUEFROG: not to worry - DT2 didn’t manage volumes, and DT3 does, which is brilliant - or would be 
@cgrunenberg: here are the steps I take and two images explaining what I mean:
In the favorites I have 4 databases listed. All 4 are located in a sparsebundle named Database.sparsebundle. The sparsebundle is password protected.
I open one of the databases by double-clicking the name in the favorites. A system dialog box requests the password to access the sparsebunde. I enter the password, click ok, the database is loaded into DT3.
Disk Utility shows the status seen in image 1.
I now close the database by right-clicking the name of the open database in the list of open databases and choosing close database.
Disk Utility shows the status seen in image 2.
The disk image is not fully ejected. If I now open any database contained in the sparsebunde I am not asked for the password again. Only once I eject the “Apple sparse bundle” from Disk Utility (remember: the “Apple sparse bundle” does not appear in Finder, whereas “Database” does, until it is ejected by DT and becomes grey in Disk Utility) do I need to re-enter the password when opening a database.
This is not resolved by restarting the computer.
Image 1:
Image 2:
