Retrading due to shift in economic backdrop?

A question for my PE folks, looking for real life practical answers: If you are waist deep in a deal, with a signed LOI at a certain price that was calculated using some trailing period EBITDA, what do you do when the macro backdrop shifts enough to suggest a lower price? The business is perfectly fine, but at the same multiple it’s implicitly overpriced now given a contraction in public multiples. Do you collect some economic doom data to justify a decrease in the offer, or do you roll with it since you’re already so far in the process and you don’t want to lose the deal.

Here’s my question instilled in a very simplistic illustration: Say an intermediary reaches out and gives you first look on an already private MM deal, such that if you turn it down, several other bidders would be interested. You like the business but recognize that it may be fairly cyclical. You end up sending in an LOI with a valuation of LTM EBITDA x a multiple of 10, which is where the company’s public market equivalents are trading. However, economic conditions quickly shift during DD and suddenly comps are trading at 6x, the likelihood of a recession is very high, and thus EBITDA will probably be lower than LTM EBITDA. The company is still quality, but you seem to be technically over paying relative to if this deal didn’t come on the market for another six months. Do you call up the seller and cite the shift in macro conditions are a reason to decrease the offer, or do you roll with it, not wanting to upset the seller and thinking you would be outbid otherwise?