I buy separate tickets all the time, especially when connecting through south-east Asia, London or Frankfurt as it often saves a fortune. However, I wouldn't dream of attempting this with anything less than an 5 or 6 hour connection as too much can go wrong and cross-linking the tickets is unlikely to help very much. Normally I would plough some of my "profit" back into an overnight stay, thus pretty much guaranteeing the connection. This also helps solve jet lag.