It's the most-commonly rejected card. It has high fees without the clout of Amex. Amex customers are typically pretty wealthy and places will accept them because of their high-roller status. But Discover doesn't have that going for them, so there's less reason to accept the card.
Where you'll find it rejected most often is small shops and government agencies.
For instance, my career has been in government, and no organization I've worked for has ever accepted Discover. We aren't allowed to "profit" from our fees, so we have to include credit card processing in the adopted fee schedule. But since we can't profit, we have to set the fee at whatever Visa and Mastercard charge. That extra 1 or 2 percent Discover charges can be millions for a large government (large city, statewide agency, etc). So, agencies simply don't take Discover (and frequently AmEx, though they'll sometimes negotiate).
Large retailers are able to negotiate better deals with Amex and Discover, but for smaller shops it just isn't gonna happen. And that 1-2% (of the total charge) extra taken by the card processor is huge when your margins are small.
Heck - even the Visa and Mastercard fees are a huge deal. When I worked in retail management, those fees were secretly the big reason we pushed our store-brand credit cards. It wasn't the 80 dollar commission for the account the store got - it was that if someone used our card in our store, we didn't pay the processing fee.
We'd give 2% in points back for using the card in the store, which was a great deal for us since we didn't have to pay the 3-4% fee to the processor.