Tomcat doesn't limit the number of users. There is a max threads but with a default value of 75, you should be able to handle hundreds or thousands of users at a time.
It is more likely that your JDBC driver or the database itself is limiting connections.
Are you using connection pooling?
Are you explicitly closing your database connections immediately after using them? If not, there is a good chance that they're not getting closed and your database is refusing connections after the 50th hit.