Well, isn’t the purpose of the candle to let people know that the Blessed Sacrament is present in the tabernacle? Being no one is allowed into the adoration chapel after hours, there wouldn’t be a need for the candle?
The candle’s purpose is twofold: it
indicates the presence of Christ (for our benefit) and it
honors the presence of Christ (for His benefit). As such, it should burn perpetually, so long as the Blessed Sacrament is present.
The precursor to the sanctuary lamp, the tabernacle lamp of the Israelites, was kept burning perpetually as well:
“And you shall command the people of Israel that they bring to you pure beaten olive oil for the light, that a lamp may be set up to burn continually.” (Exodus 27:20)
“Command the people of Israel to bring you pure oil from beaten olives for the lamp, that a light may be kept burning continually. Outside the veil of the testimony, in the tent of meeting, Aaron shall keep it in order from evening to morning before the LORD continually; it shall be a statute for ever throughout your generations.” (Leviticus 22:2-3)
In Job 21:17, we read “How often is it that
the lamp of the wicked is put out? That their calamity comes upon them?” In Proverbs 13:9, we read “The light of the righteous rejoices, but
the lamp of the wicked will be put out.” Putting out a lamp was a symbol of death or at least of absence of presence. The sanctuary lamp is a symbol of the Lamb in Revelation 21:23: “And the city has no need of sun or moon to shine upon it, for the glory of God is its light, and
its lamp is the Lamb.”
I think it is proper, then, that the sanctuary lamp be kept burning perpetually, even when no one
visible is there to see it.