Looking back in our blog, I see that I installed a Dometic LED light strip under our awning on April 30, 2013 (13 months now). It has become our go-to 'porch light'. We leave it on hours at a time, sometimes a day or two, and have noticed no ill effects.
On the other hand this is not the same light strip used by HL on the OEM units, so it's not really a valid comparison. In general, though, LED light strips should be able to be left on for long periods of time without ill effect.