SSMS IntelliSense doesn't work on particular database
It might be latency, or it might be something else. Run a SQL Server Profiler trace on the remote DB, starting the trace just prior to connecting via SSMS remotely. IntelliSense works by running queries to get the meta-data, so you will be able to see if it is even attempting to work or not, and if so, potentially if it is running into any problems.

You should filter the ApplicationName column on LIKE %IntelliSense%, though the full name of the program is Microsoft SQL Server Management Studio - Transact-SQL IntelliSense. Events to select: SQL:BatchStarting, SQL:BatchCompleted, SQL:StmtStarting, SQL:StmtCompleted, SP:Starting, SP:Completed, SP:StmtStarting, SP:StmtCompleted, RPC:Starting, and RPC:Completed.

Try it first on a DB that works so you know what the normal / expected behavior should look like. Hitting Control + Shift + R to force a reload of the local cache should produce a decent amount of activity captured by your trace.