why should brahmins consider it as a duty to perform sandhyavandhanam and arghyam by Gayatri.

॥रक्षांसि ह वा पुरोनुवाके तपोग्रमतिष्ठन्त तान् प्रजापतिर्वरेणोपामन्त्रयत तानि वरवृणीतादित्यो नो योद्धा इति तान् प्रजापतिरब्रवीद्योधयद्ध्वमिति तस्मादुत्तिष्ठं तं ह वा तानि रक्षांस्यादित्यम् योधयन्ति यावदस्तमन्वगात्तानि हवा एतानि रक्षांसि गायत्र्याभिमन्त्रितेनांभसो शाम्यन्ति तदुहवा एते ब्रह्मवादिनः पूर्वाभि...मुखाः सन्ध्यायाम् गायत्र्याभिमन्त्रिता आप ऊर्द्ध्वं विक्षिपन्ति ता एता आपो वज्रीभूत्वा तानि रक्षांसि मन्देहारुणे द्वीपे प्रक्षिपन्ति यत्प्रदक्षिणं प्रक्रमन्ति तेन पाप्मानमवधून्वन्त्युद्यन्तमादि​त्यमभिध्यायन् कुर्व्वन् ब्राह्मणो विद्वान् सकलं भद्रमश्नुतेऽसावादित्यो ब्रह्मेति ब्रह्मैव सन् ब्रह्माप्येति य एवम् वेद॥

हारीतेनोक्तं
आदित्येन सहप्रातः मन्देहानाम राक्षसाः।
युध्यन्ति वरदानेन ब्रह्मणोऽव्यक्तजन्मनः॥
उदकाञ्जलिनिक्षेपात् गायत्र्याचाभिमन्त्रितः।
निघ्नन्ति राक्षसान् सर्वान् मन्देहाख्यान् द्विजेरिताः॥
ततः प्रयाति सविता ब्राह्मणैरभिरक्षितः।
मरीच्याद्यैर्महाभागैः सनकाद्यैश्च योगिभिः॥
तस्मान्नलङ्घयेत् सन्ध्यां सायं प्रातः समाहितः।
उल्लङ्घयति यो मोहात् स याति नरकं ध्रुवं॥
Once some demons were desirous of fighting with the Sun and with a view to gain the requisite strength for the battle, they propitiated Brahmadeva with hard penance. Brahmadeva appeared and asked the demons to take any boon they wanted. They selected through the boon the strength to fight with Sun. Immediately they started a battle with Sun. If the Sun was to win in the persistent battle with these demons from dawn to dusk, the only way was to sprinkle these demons with water sanctified with the chanting of Gayatri. The Brahmins perform the sprinkling of water through the arkhyam and drive away the demons called mandehaas to the Island of Aruna. Even today Brahmins are doing this arghyam with a view to ensure that the Sun is not debilitaated through the attack of the demons. Thus say the Vedas.
Haareetha, a sage and a lawgiver  has also given the same description elsewhere.
"A group of demons named mandehas start fight with the Sun right from the morning, deriving strength from a boon given by Brahma. The people called Brahmins defeat those demons through pouring water up with the chanting of Gayatri. Therefore the Sun is going the round from dawn to dusk only because He is protected by the Brahmins performing the arkhyam, and this is done by the god-like mareechis, and yogis lika sanakas and others . It is the duty of every brahmana to give the arkhyam to save the Sun and thereby save the universe.This is the most important part of the Sandhya rituals performed by the Brahmins.
Therefore the practice of giving arkhyas in the morning and evening should never be breached. If any Brahmin does so, through forgetfulness or arrogance, he will surely find naraka or hell as his final destination.