Part of an ongoing series of 5e Rules notes.

The range and need of line-of-sight is pretty clear when spells are initially cast, but what happens if range is exceeded or line of sight is broken in a spell that lasts more than an instantaneous effect — in particular, with spells that require Concentration to maintain them?

(In the case that came up in my campaign, the party wanted to maintain a spell as they fled; a more common instance is the affected party fleeing the caster and breaking LoS or exceeding distance.)\

The General Rule

It’s pretty straightforward:  range and line-of-sight don’t matter once the spell has been cast. As PHB 203 puts it:

Once a spell is cast, its effects aren’t limited by its range, unless the spell’s description says otherwise.

So, as a general rule (and as confirmed by Jeremy Crawford and also confirmed by Jeremy Crawford), once you have successfully cast a spell on a spot or a target opponent, it will continue until it naturally ends (i.e., with a Concentration spell, until the time limit is passed or the character drops concentration), regardless of what the range or line-of-sight is. You are maintaining the spell, not the targeting.

Spells that say otherwise, of course, are otherwise (the specific overrides the general).

That said, if you and the target are beyond LoS, you don’t know what is going on there. Maybe the guy you threw Heat Metal on ran into the next room, took off the armor, and put it on an orphan waif, and your continuing the damage is killing an innocent. Ah, well …