Limiting the number of connections for one user

Hello,

We clearly have a bug in our application: sometimes for reasons we
have not been able to understand yet, the application will start
creating connection like madness (several dozens in a matter of
minutes). This eats up too quickly the number of connections we have
available on the server and is not healthy anyway.

We have narrowed the problem down to only 2 users having had this
issue over the past few days.

Whilst we are investigating what happens I am wondering if there are
anyway to limit the number of connection a specific IP address can
make to a server; this would not solve the user's issue but prevent it
from spreading and affecting every other users.

I googled but did not find anything remotely related to this.

Thanks for your thoughts

Didier