Postgresql huge remote connections raise "connection to server at "host",port 5432 failed Connection timout Is the server accepting TCP/IP connections

Question

I created database on separated server, and i have another remote three servers that connected with the database, i have huge connections that occurred in same time from those three servers, many of them can finish the query successfully but sometimes raise error "connection to server at "000.000.000.000", port 5432 failed: Connection timed out Is the server running on that host and accepting TCP/IP connections?"