Hana

The renewal baseline is the trap. Going back up is a price rise to them, however you frame it.

The costs beyond the money, since that was your actual question.

Renewal. Whatever you agree becomes the baseline. Going from a discounted price back to full at renewal is a price rise from their side, and it is a difficult conversation you have created for yourself twelve months out. If you discount, state the term explicitly: this rate applies to the first year: in writing, in the agreement.

Precedent inside their company. The person who negotiated it will mention it, and the next department that buys will start from that number.

Precedent with your other customers. Less of a risk than people fear, and not zero - public discounting becomes known, and your full-price customers are the ones who find out.

Your own anchoring. The uncomfortable one. Once you have discounted for a big logo you will do it again, and after three of those your list price is decorative.

What it does not cost: the relationship. A polite no does not offend a professional buyer.

So my suggestion for your specific case: offer the twenty percent for a two-year commitment paid annually up front, or the same price with a named case study. Either is a yes that costs you nothing you cannot afford, and both leave your price intact.