My aunt refused to pluck a leaf from the Tulsi plant after sundown and when I asked her for a reason, she gave an answer with which I was not satisfied at all. So can anybody tell me if we should not pluck leaves of Tulsi plant after sundown or if there is no rule as such.
Your aunt did the right thing.
Plucking Tulasi leaves after sunset and at certain other times is strictly prohibited as per our scriptures & is considered to be a big offence. The Devi Bhagawatha Purana (in Book 9; 24th Chapter) states that:
Whoever holds in his neck the garland made up of Tulasî wood, gets certainly the fruit of horse sacrifices at every step. He who does not keep his word, holding the Tulasî leaf in his hand, goes to the Kâlasûtra Hell as long as the Sun and Moon last. He who gives false evidence in the presence of the Tulasî leaf, goes to the Kumbhîpâka Hell for the life-periods of fourteen Indras. He who drinks or gets a bit of the Tulasî leaf water at the time of death, certainlygoes to Vaikuntha, ascending on a car made up of jewels. Those who pluck or cull the Tulasî leaves in the Full Moon night, on the twelfth lunar day, on the passing of the sun from one sign to another, the mid-day, or on the twilights, on the night, while applying oil on their bodies, on the impurity periods, and while putting on night dresses, verily eat off the Nârâyana’s head.
Edit-Adding one more source.This one is from the book called "Essence of Dharma Sindhu:
Tulasi Mahima: As regards Tulasi, it is stated that during the Vaidhruti and Vyatipata times, Sunday-Tuesday-Fridays, Purnima and Amavasyas, Sankranti days, Dwadashi Tithis and during Ashuchi days, plucking Tulasi is as atrocious as cutting one’s own head. Plucking Durva on Sundays, Tulasi on Raatris and Sandhyas, Dhatri Patra in Kartika Month, no person desirous of achieving Punya would never attempt.
In Sri Vaishnava practices, even on permitted days, the Tulasi is plucked only in the morning and never in the afternoon.
In the Srivaishnava Sadachara Nirnaya by Sri Narayana Yatindra Mahadesikan, a Smriti verse is quoted:
āravāre ca śukre ca manvādiṣu yugādiṣu
nāharet tulasīpatram madhyāhnātparatastathā
nāharet = do not pluck
madhyāhnātparatastathā = in the remaining portion of the day after noon.
The author doesn't quote the name of the Smriti but the verse appears to be from the Bhrigu Samhita (35.533) http://gretil.sub.uni-goettingen.de/gretil/1_sanskr/4_rellit/vaisn/bhrgus_u.htm