>>Leaving the connection "open" is the closest that you can get to leaving
>>a VFP table open. Although, this is almost like comparing apples to oranges.
>>
>>In SQL Server, one of the more expensive operations (in terms of time spent) is opening the connection to the server. In desktop applications is a common practice to open the connection once (as soon as the app is launch) and leave it open during the session to improve performance. There is an option to share this connection accross all views and queries to the backend. This way you will only use one connection per user (which might be acceptable on certain scenarios but not in others.)
>
>Yes, I see the first connection takes time. But, the most important is that whatever will follow will be optimized. That scenario fits ok in Web applications. But, the main question is if there is a timeout. Basically, if one Web application opens the connection at once and then a series of hit to process SQLs on the server is done, will I loose this connection at one time with a timeout?

Yes, there are time out values that you can set. The following article gives a good overview of how this works and how to use connection pooling to optimize scenarios like yours:

http://msdn.microsoft.com/library/default.asp?URL=/library/techart/pooling2.htm