Concurrent connections for any shared hosting account is currently limited to 20. This is not the number of users allowed on your site at a time, but instead the limit for users who are attempting to connect to a PHP or Perl script. 20 concurrent connections would be more than 20 requests a second, assuming the page takes one second to load.
To put it another way, 20 visitors would need to visit your site at the same moment to hit the limit. If your account is outgrowing this limit, then you have outgrown a shared hosting environment.