• brahma-āsanam — the seat of brahman / spiritual teacher
  Brahma (here = the supreme/teacher) + āsana (seat). The seat the sages had bestowed on Romaharṣaṇa. This explains why he was sitting above brāhmaṇas — they had elevated him. The geometry was their gift; the conduct was his failure.
• yadu-nandana — O joy of the Yadus
  Yadu + nandana (delight, son). Vocative address. They invoke Balarāma's Yadu-affiliation precisely while reminding Him of obligations to brāhmaṇas — a gentle pressure point.
• āyuḥ — lifespan
  Āyus — Vedic vital duration. The sages had promised him āyuḥ; the Lord will need to restore equivalent vital quantum, which He does by transferring it to his son in v.36.
• ātma-aklamam — freedom from physical pain
  Ātma (body/self) + a-klama (un-fatigue, freedom from exhaustion). The second item of the vow. Klama = exhaustion. The sages had pledged he would not tire mid-satra; the Lord must replace this too.
• satram samāpyate — until the sacrifice is completed
  Satra + samāpyate (passive of sam-√āp, 'reach completion'). The duration of the vow. The Lord's responsibility is bounded by the duration of the rite — He must arrange that the satra completes intact.

• Where do I dismiss authority that the community has genuinely granted?
• How do I honor the position even when its holder is unworthy?

The sages had given Romaharṣaṇa the brahma-āsana, the very seat of the spiritual teacher — and a vow of long life, freedom from bodily pain, for as long as the satra lasted. When the Lord kills him, He has also broken their vow. The accusation is in fact two accusations folded into one: against their guest, but also against their own pledge.