You have not mentioned what unicast and multicast control planes you are using, but 1 second multicast reconvergence is not unreasonable without optimizations for fast reconvergence. I will assume for the moment that you are running some IGP (OSPF/IS-IS/EIGRP) and some form of PIM (Sparse Mode or SSM) as your control planes.
Once the MDT (multicast distribution tree) is built from the receiver to the source's first-hop router either directly (SSM) or indirectly via RP (Sparse Mode), when a topology change occurs along the path of the MDT, the IGP must reconverge, followed by PIM. However, reconvergence cannot take place until the topology change is first detected. Rapid detection capabilities will be dependent on your platform's implementation and I do not have experience with NX-OS to say for certain what it can do, but it usually comes down to BFD or routing protocol timer expiry tweaks, with BFD typically being the fastest notification method (BFD sessions can often be offloaded to hardware for supporting timers in the low milliseconds). After BFD notifies its clients (control plane routing protocols like your IGP and/or PIM) of the link failure, the client processes can begin reconverging on the new topology and the multicast packets can resume over the new MDT.
You can likely get plenty of advice in this forum (or from your Cisco account team or Services team) on how to optimize your IGP for fast reconvergence, but you will need to supply more details.
Disclaimers: I am long in CSCO. Bad answers are my own fault as they are not AI generated.