We are also using SQL Prompt v18.104.22.168 within our organization and are experiencing a similar issue.
When a SQL file is opened within an SSDT project in VS 2010, SQL Prompt suggestions work for SQL Keywords, local stored procedure variables, etc. In order to get suggestions for database objects, we need to connect to the database using the Connect to Server menu item...
Once connected to the database, SQL Prompt works correctly, but as soon as a new file is opened, we need to use Connect to Server again.
Because of this, it's actually more convenient to disable SQL Prompt suggestions and use the intellisense provided by SSDT. However, each time we open the SSDT project we have to enable SSDT intellisense. SSDT intellisense seems to be defaulting to disabled since we installed SQL Prompt.