There are many such occasions and days when Veda study is forbidden. Those are enumerated in Manu Smriti 4.101 onwards:
4.101. Let him who studies always avoid (reading) on the following occasions when the Veda-study is forbidden, and (let) him who teaches
pupils according to the prescribed rule (do it likewise).
Then the text gives a long list of forbidden occasions:
4.102. Those who know the (rules of) recitation declare that in the rainy season the Veda-study must be stopped on these two (occasions),
when the wind is audible at night, and when it whirls up the dust in
the day-time
4.103. Manu has stated, that when lightning, thunder, and rain (are observed together), or when large fiery meteors fall on all sides, the
recitation must be interrupted until the same hour (on the next day,
counting from the occurrence of the event)
4.104. When one perceives these (phenomena) all together (in the twilight), after the sacred fires have been made to blaze (for the
performance of the Agnihotra), then one must know the recitation of
the Veda to be forbidden, and also when clouds appear out of season.
4.105. On (the occasion of) a preternatural sound from the sky, (of) an earthquake, and when the lights of heaven are surrounded by a halo,
let him know that (the Veda-study must be) stopped until the same hour
(on the next day), even if (these phenomena happen) in the (rainy)
season.
4.106. But when lightning and the roar of thunder (are observed) after the sacred fires have been made to blaze, the stoppage shall last as
long as the light (of the sun or of the stars is visible); if the
remaining (above-named phenomenon, rain, occurs, the reading shall
cease), both in the day-time and at night.
4.107. For those who wish to acquire exceedingiy great merit, a continual interruption of the Veda-study (is prescribed) in villages
and in towns, and (the Veda-study must) always (cease) when any kind
of foul smell (is perceptible).
4.108. In a village where a corpse lies, in the presence of a (man who lives as unrighteously as a) Sudra, while (the sound of) weeping (is
heard), and in a crowd of men the (recitation of the Veda must be)
stopped.
4.109. In water, during the middle part of the night, while he voids excrements, or is impure, and after he has partaken of a funeral
dinner, a man must not even think in his heart (of the sacred texts).
4.110. A learned Brahmana shall not recite the Veda during three days, when he has accepted an invitation to a (funeral rite) in honour of
one ancestor (ekoddishta), or when the king has become impure through
a birth or death in his family (sutaka), or when Rahu by an eclipse
makes the moon impure.
4.111. As long as the smell and the stains of the (food given) in honour of one ancestor remain on the body of a learned Brahmana, so
long he must not recite the Veda.
4.112. While lying on a bed, while his feet are raised (on a bench), while he sits on his hams with a cloth tied round his knees, let him
not study, nor when he has eaten meat or food given by a person impure
on account of a birth or a death
4.113. Nor during a fog, nor while the sound of arrows is audible, nor during both the twilights, nor on the newmoon day, nor on the
fourteenth and the eighth (days of each half-month), nor on the
full-moon day.
4.114. The new-moon day destroys the teacher, the fourteenth (day) the pupil, the eighth and the full-moon days (destroy all remembrance
of) the Veda; let him therefore avoid (reading on) those (days).
4.115. A Brahmana shall not recite (the Veda) during a dust-storm, nor while the sky is preternaturally red, nor while jackals howl, nor
while the barking of dogs, the braying of donkeys, or the grunting of
camels (is heard), nor while (he is seated) in a company
So, as far as the monthly days are concerned, Purnima, Amavasya, two Chaturdashis and two Ashtamis are stated as forbidden days for Veda study.
EDIT:
List of occasions when Vedic study needs to be suspended is found in Gautama Dharma Sutras 16.5--16.49 as well:
5 He should suspend vedic recitation during daytime when the wind
whirls up the dust; 6 at night when he can hear the wind blow; 7 when
the sound of a lute, drum, side drum, chariot, or wailing is heard; 8
when dogs are barking, jackals are howling, and donkeys are braying; 9
when the sky turns crimson; when a rainbow appears; when there is
frost on the ground; 10 when clouds appear out of season; 11 when he
has the urge to void urine or excrement; 12 in the middle of the
night, at the time of twilight, and while standing in water; 13 when
it is raining–– 14 but, according to some, only when the water is
running down the eaves––; 15 when Venus and Jupiter are surrounded by
halos, 16 as also the sun and the moon; 17 when he is frightened,
travelling in a vehicle, lying down, or has lifted his feet; 18 when
he is in a cremation ground, at the village boundary, on a highway, or
in an impure state; 19 when there is a foul smell; when there is a
corpse or a Chandala in the village; when a S´udra is near by; 20 and
when he experiences an acrid belching.21 The recitation of the Rgveda
and the Yajurveda, moreover, is suspended as long as the recitation of
the Sa¯maveda is heard.
22 When there is a lightning strike, an earthquake, an eclipse, or the
fall of a meteor, vedic recitation is suspended until the same time
the next day; 23 as also when there is thunder, rain, or lightning
during twilight when the fires are visible. 24 When these happen
during the rainy season, however, the suspension lasts only that day.
25 When there is lightning during the night, moreover, the suspension
lasts until the last watch of the night; 26 but if it occurs during or
after the third part of the day, the suspension lasts the whole night.
27 According to some, a meteor has the same effect as lightning with
respect to the suspension of vedic recitation, 28 as does thunder when
it occurs in the afternoon 29 or even at dusk. 30 If there is thunder
before midnight, the suspension lasts for the whole night; 31 if it
happens during the day, the suspension lasts throughout the daylight
hours, 32 as also when the king of that realm dies, 33 and when one
student goes on a journey and another stays behind with the teacher.
34 The suspension lasts for a day and a night when there has been a
social disturbance or a fire; when he has finished reciting one Veda;
when he has vomited; when he has eaten at an ancestral offering or at
a sacrifice to humans ; 35 on the new-moon day–– 36 alternatively, the
suspension here may last for two days––; 37 and on the full-moon days
of the lunar months October–November, February–March, and June–July.
38 At the three eighth-day offerings during the three fortnights of
the waning moon following the full moon of November– December, the
suspension lasts for three days; 39 according to some, the suspension
takes place only at the last of these eighthday offerings. 40 When the
annual course of study is commenced and concluded, the suspension is
in effect on that day, as well as on the preceding and following days.
41 In the opinion of all authorities, when rain, lightning, and
thunder occur together, the suspension lasts for three days, 42 as
also when there is heavy rain. 43 On a festive day vedic recitation is
suspended after the meal. Immediately after commencing the annual
course of study.recitation is suspended during the first four ‘hours’
of the night. 45 According to some, vedic recitation is always
suspended in a town. 46 Even mental recitation is suspended when a
person is impure. 47 After making an ancestral offering, the
suspension lasts until the same time the next day, 48 as also when
uncooked food is distributed at an ancestral offering. 49 Vedic
recitation is also suspended for reasons given in each vedic branch.
