So TO‘s firewall can‘t be the problem as it would either work or not if this would be the problem…
It sounds like a discovery problem… I don’t know your tv box so I can only guess it could use ICMP, avahi or some vendor specific protocol to discover your cable modem. So you could need some kind of ICMP or avahi proxy service running on your TO, which is possible to set up (although out of my knowledge).
I know that some TV boxes only work stable if IGMP snooping is enabled (LuCI → Network → Interfaces → LAN-Interface → Physical settings → enable IGMP snooping).
Which TOs version are you using? There are some connection issues with TOS 5.X on its internal switch, you could try to switch your Ports so that your cable modem is connected to LAN4 Port and your switch is connected to the WAN Port of your TO. See this post for instructions: Turris OS 3.11.23 -> OS 5 - recommended to wait due to issues? - #4 by protree - SW help - Turris forum
Again, is your cable modem running in modem (bridge) mode or router mode? If it runs in router mode you could bridge its network to your tv box through a vlan but this would require managed switches.
These are just some ideas, but maybe one of them will point you into the right direction 