What are the benefits, physical or mental, material or spiritual? Also, what are the consequences of not doing it?
After the initiation into the Gayatri Mantra (i.e after Upanayana), for the Dvijas, performing Sandhya becomes a Nitya Karma - which means a rite that one has to perform daily without fail.
Failure means accumulation of sins and falling from the caste etc. Benefits of performing it daily is obviously getting rid of all the sins, remaining healthy, and getting exalted status after death etc.
These things are summed up in the following two Manu Smriti verses:
2.102. He who stands during the morning twilight muttering (the Savitri), removes the guilt contracted during the (previous) night; but he who (recites it), seated, in the evening, destroys the sin he committed during the day.
2.103. But he who does not (worship) standing in the morning, nor sitting in the evening, shall be excluded, just like a Sudra, from all the duties and rights of an Aryan.
So, one who is initiated but not performing Sandhya daily is to be treated as a Sudra for all purposes.
Actually, one who does not perform Sandhya daily is not considered fit to perform any other religious rites. This thing is mentioned in the following verses from Devi Bhagavata Purana 9.26 :
Do this Japam, being pure, everyday in the morning, mid-day, and in the evening. If one be impure and devoid of Sandhyâ, one has no right to do any action; and even if one performs an action, one doesnot get any fruit thereby. He who does not do the morning Sandhyâ and the evening Sandhyâ, is driven away from all the Brâhminic Karmas and he becomes like S’ûdras. He who does Sandhyâ three times throughout his life, becomes like the Sun by his lustre and brilliance of tapas. What more than this, the earth is always purified by the dust of his feet. The Dvîja who does his Sandhyâ Bandanam and remains pure, becomes energetic and liberated while living. By his contact all the Tîrthas become purified. All sins vanish away from him as snakes fly away at the sight of Garuda. The Dvîja who becomes void of Sandhyâ three times a day, the Devas do not accept his worship nor the Pitris accept his Pindas.
Those who eat without washing their feet or those who sleep with their feet wetted with water and those who eat just after the Sun has risen, commit Gohattyâ. Those who eat the food of women without husbands or sons or the food of pimps and pampers or those who do not perform their Sandhyâs thrice, commit Gohattyâ.
and, the following verses from the same Purana says, if a Brahmin fails to do Sandhya for just three days, he degrades himself to a Sudra.
Without this bath, no acts bear any fruit. Therefore everyday, this morning bath is very necessary. Taking the Kus'a grass in hand, one is to perform one's bath and Sandhyâ. If for seven days, the morning ablutions are not taken, and if for three days, the Sandhyâs are not performed, if for twelve days, the daily Homas be not performed, the Brâhmanas become S’ûdras.
Devi Bhagavata Purana 11.3
Further verses from Baudhayana Dharma Sutras 2.7.11, giving the benefits of performing Sandhya Vandanam daily, are as follows:
In that event, a man should fast during the night if he neglects the evening twilight worship and during the day if he neglects the morning twilight worship.
He obtains thereby the reward of standing during the morning and sitting during the evening twilight worship.
Now, they also quote:
Whatever sin a man may have committed through his sexual organ, feet, arms, mind, or speech, he frees himself from it by worshipping the evening twilight.
He also unites himself with the night, and Varun. a does not seize him. Likewise, by worshipping the morning twilight he frees himself from sins committed during the night. He also unites himself with the day; Mitra, moreover, protects him, and Sun leads him up to heaven. ‘When in this manner a Brahmin worships during the twilights between the day and the night,’ it is stated, ‘he becomes purified by Brahman; he becomes Brahman; and, abiding by the dictates of scripture, he wins the world of Brahman