Does going outside of range or line of sight after casting a spell have any effect?

Does going outside the range of the spell or breaking line of sight between the caster and target break concentration or otherwise affect control over the spell?

For example, a Heat Metal spell has a range of 60 ft. If I cast the Heat Metal spell on a an armored foe, and that foe runs outside the range of the spell (60 ft), or around the corner, does that break concentration and end the spell? Heat Metal also allows you to use a bonus action to cause the 2d8 of damage — would exercising that option be prevented by being out of range or line of sight?