I managed to get the stopover visa once via the SV website. I had booked directly with SV and later pushed the button extra services and could apply and pay for the visa, and got it instantly.

Later I had tickets booked via an OTA, and the SV website did not let me pay or gave a technical error when applying for the visa.

I then tried www.ksavisa.sa, that allows Dutch like me to apply for a stopover/transfer visa for 25 Euro as well. That ended up in a nightmare - apparently the Embassy in the country where you live is to be involved and in my case even after a bunch of mails nothing worked out, and by now they neglect my mails. Based on my experience I do not trust this route for getting a stopover/transfer visa. I sent them another polite mail that I appreciate the efforts of opening the KSA for tourists (the Messi clip they show in the Alfursan lounge on wrong impressions of the Kingdom is really nice) but that clear instructions and giving clear expectations what it takes to get your visa on the ksavisa.sa is essential, that things should be reliable, and you never should have people ending up in a situation that they pay 25 Euro's and then never hear back (how limited the loss is). It just does not make a professional, welcoming impression.