I'm not immediately aware of any system that does this, since electing a leader when both the current leader is functioning properly and all functioning workers are able to talk to the leader (i.e. there is no network partition) is unnecessary overhead.
However, it should be easy to add this functionality to an existing system, such as Raft. Section 5.2 describes the leader election process. An election is only triggered when a worker does not receive a heartbeat from the leader for a certain amount of time (the election timeout). You can simply add a condition that also triggers an election when the fixed interval of time you reference in your question has passed.
You can modify other systems in a similar way to achieve the same result.