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Originally Posted by sclitheroe

Ironically, this can actually be an issue. The router needs to maintain a table in memory that links external connections to the internal hosts that have initiated or accepted them (the NAT translation table). If you exceed the capacity of the router to track all the entries required in this table, you can see all kinds of weird issues, such as dropped connections, inability to make additional new connections, router crashes, etc.

Torrents and game server browsers are two examples of applications that generate a huge number of NAT translation table entries. Multiple hosts inside the home network all using torrent or game browser software could overload the NAT translation table and cause the issues described. Malware could also exhibit this behavior as it tries to "reach out and touch someone"

I don't know which modern routers might be affected by this - its not really a stat that home router manufacturers advertise.

I think in this case, its cheap components in the router overheating or having failed, but if the issue only exists when multiple machines are active, it might be worth investigating.

Jerk! Good to know though.