Does depending on one key supplier hurt my asking price the way customer concentration does?

Yes, generally for a similar reason — a buyer is being asked to rely on a relationship they don't control and didn't negotiate, and if that single supplier increased prices, changed terms, or walked away, the business's earnings could be affected in a way that has nothing to do with how well the new owner runs things. That's a risk buyers price into their offer just as they do with a concentrated customer base.

The nuance is that not all supplier dependency looks the same to a buyer. A single supplier providing a commodity input that's genuinely available from several alternative sources is a much smaller risk than a single supplier providing something specialized, exclusive, or tied to a personal relationship you've built over years that may not transfer to a new owner. Buyers and their advisors will typically ask how easily that relationship could be replaced.

If a key supplier relationship is central to your business, it's worth thinking, before you sell, about whether the terms are documented in a written agreement rather than resting on an informal understanding, and whether there are realistic alternative suppliers you could point to. A business lawyer can help you review what's actually in writing and where the real exposure sits.