How can I connect to a database after its disk has come back online?
First, tell your customer to get a real disk. Using a remote disk this way is exactly why you are having difficulty at this stage, and it could very well lead to a corrupt / unrecoverable database. You are rolling the dice every time this drive goes offline, even if only temporarily.
Next, check the status of the database:

USE master;
GO
SELECT state_desc 
  FROM sys.databases
  WHERE name = N'your_database';


If this if OFFLINE, and you're sure the drive is available, run:

ALTER DATABASE your_database SET ONLINE;


Now, this might not work - as I suggested the database could come up SUSPECT or it might not come online at all.
If / when it does come back online, take a full backup. Schedule these (and/or log backups if in full recovery) to run much more frequently, to cover your butt.
Tell your customer to get a real disk. This may work in the short term but this is a ticking time bomb.