Hello Horacio,
I do not fully understand your setup from your description. If a port goes down then it does not carry data. However, all other ports on the same switch and on other switches in the stack should not be influenced, and they should be able to carry data without problems. So if your server is connected to your switches via multiple ports, the remaining ports should allow the server to have uninterrupted connectivity.
Note, however, that usually a special support on the server side is needed to make use of multiple connections to the same network (e.g. channel bonding in Linux, NIC teaming in MS products).
Best regards,
Peter