In our situation replication doesn't run continuously. It's scheduled for the night and it runs a few times a week. To my opinion that's better because also the data in the publisher is updated only a few times every week.

And yes you're right, SQL server is working and some data can be retrieved from the tables. But in most cases it takes a very long time for (some relatively simple) stored procedures to run. This will end up with a timeout error on the website.

I hope the problem is a bit more clear now.