This happens quite regularly for multi-carrier trips. Less so for single carrier trips.

Airline search algorithms are often inferior

For single carrier trips, it's almost always because the airline's search algorithm doesn't find the trip you want, not because the airline doesn't sell it.

If the search tool is an in-house product, it may be inferior in an absolute sense compared to something like ITA's QPX search, which many OTAs now use. Writing a search algorithm for airline flights is a terrifically hard problem (formally it is classed as "undecidable"), and airlines don't hire the kind of computer scientists who can solve it efficiently. Specialists like ITA have hundreds of computer scientists.

Alternatively, an airline's search may be tuned with different preferences to an OTA. A lot of airlines try to avoid overnight stops, even if that would be preferable to three flights at a higher price. I would guess that's the cause of your SAS problem here.

Solutions

1. Try the multicity search, and put some of the connecting cities in as if they were stopovers. When you choose the dates, choose the dates that you'll actually fly that leg. This is often a good bet, but it sometimes causes the airline to price your trip with a fare break point at the stopover (i.e., as a sum of one way fares instead of a single through fare): Iberia.com is particularly terrible for this shortcut. However, I notice SAS has helpfully removed its multicity feature as part of the dumbing down exercise that makes the rest of its webpage unusable on a real computer.

2. Bookwithmatrix or Google Flights can sometimes link you directly to the desired itinerary on the airline's site. (If you do this on aa.com, you'll find that you get kicked out at the payment stage if your credit card's address isn't in the United States. But it turns out AA doesn't actually validate the country field, so you can just leave it set to United States.)

3. Call the airline, tell them what flight numbers you want to fly, and give them the price you expect. There is usually a telephone booking fee for doing this, although if you have some status with the airline it might be waived, particularly if you explain their website was not good enough to do it online. I used to have a friend at the Amsterdam ticketing desk for British Airways. In what I consider a crowning achievement some years ago, I constructed a price for a trip from information on expertflyer.com that was 50% lower than his system or any OTA admitted, and after some back and forth with revenue management, he agreed it was a bug in their pricing system and sold me the itinerary at the lower price. :-)

(and if so, would this be standard practice, or should I expect it to be hit and miss depending on the airline?)

BA, AA, KLM, 90% success rate, sometimes have to hang up and call again. Qantas, JAL, Cathay Pacific, their telephone staff and ticket desks are always reliable. Air France, maybe 50%. Iberia, Alitalia, LATAM: total waste of time.

Point-of-sale differences in inventory

Sometimes, additional inventory is available in the city where the travel agent is based, compared to where the airline is calculating the price. To understand why that can be the case, you should know that "how many seats left for sale on a plane" is a function of the sales city as well as other factors. Airline websites, in my experience, usually price from the city of origin, whereas agents usually price from a fixed point. One way to see this is from the payment currency, which will invariably be the currency of the sales city. For instance expedia.fr prices out of Paris, regardless of whether the itinerary passes through that city.

This only seems to matter when the flight is filling up.

Ticket issuance restrictions in the fare

Sometimes, the airline really cannot sell you the trip. This may be because the trip comprises multiple fares and one of the fares has a restriction that it must be issued "on the stock" of a ticket airline. Stock here refers to the old fashioned 4-part carbon paper tickets, but the concept is directly implemented in electronic ticketing. For instance, looking at a cheap S7 fare from London to Yekaterinburg:

Category 15: Sales restrictions
  TICKETS MUST BE ISSUED ON S7.
         NOTE -
          SALES PERMITTED ON TICKET STOCK VALIDATED OR
          PLATED S7/421 ONLY.

Even though a BA plane will fly you the first leg from London to Moscow, BA could not sell you a journey involving this particular fare. Airlines always sell tickets on their own "paper", not as agents for another airline; in this case, BA sells tickets on BA plate (ticket number starting "125-") and S7 sells tickets on S7 plate (ticket number starting "421-"). But a travel agent could pick any validating carrier with whom it has a ticketing agreement, subject to the fare rules and the agreement. So the travel agent has some additional flexibility.

This really only matters when you have a particularly complicated trip with multiple airlines who don't partner together very closely.