A hard drive that is used as little as possible will likely last longer. If it's just for storage it shouldn't tax the hard drive too much, but I wouldn't recommend seeding for long periods of time off an external.
I greatly prefer mounting hard drives internally, and the basis of this preference is the increased cooling capacity provided by a good computer case (8cm-or-larger fan for ventilating hard drives, v.s. 4cm-or-smaller fan in an external enclosure, if not none at all).
On this premise, internally-mounted hard drives without forced ventilation are not much better than hard drives in an external cage (this is usually the case in a basic super-cheap computer case, and possibly in some budget pre-builts as well). If ambient temperatures and humidity are really low there, you might be able to get away with it. But I live in the tropics; humidity is typically >80%, and temperatures never go lower than 25˚C—no way I'm going to risk hard drives going unventilated here.
[Confession: Okay, so I do have an unventilated external... but I don't use it for seeding, and it's currently only being used to archive some raw data.]If you have
SMART reporting on your hard drives, check the drive temperatures. Anything above 50˚C is way too hot (unless it's an enterprise drive designed to withstand such temperatures over 24/7 operation… but why would you put such a drive in an external enclosure?), and personally I try to keep it no more than 45˚C. Ideal temperatures are probably in the 30˚C region (depending on your regional climate).
Note that even if you follow the guidelines above it is no guarantee against disk failure (just like there is no 100% guarantee against heart failure), but you certainly lower the risk of it happening by quite a bit (I think).